"The eradication of terrorist organisations will lead to the political solution that Syria and Russia seek and that will satisfy the Syrian people and preserve Syria's sovereignty, independence and territorial integrity," he said, quoted by news agency SANA.
The visit by Russian lawmakers came days after Assad made a surprise trip to Moscow for talks with President Vladimir Putin.
That trip and ramped-up Russian diplomacy have led to speculation that Moscow is pushing for a new political agreement to end the conflict that began with protests against Assad's rule in March 2011.
But the shape of any such deal remains unclear, with Syria's opposition firmly against Moscow leading peace efforts while pursuing an air campaign it launched in support of Assad on September 30.
A Russian lawmaker said Sunday that Assad had expressed a willingness to hold new parliamentary and presidential elections, but only after Syria is "liberated" from Islamic State group jihadists.
"He is ready to conduct elections with the participation of all political forces who want Syria to prosper," the lawmaker Alexander Yushchenko told AFP.
Assad would run again "if the people are not against it," he added.
- Opposition dismisses new vote -
Russian Foreign Minister Sergei Lavrov has said that Syria needed to begin preparing for new elections.
Syria last held parliamentary polls in May 2012, with the next one planned for 2016.
A presidential election was held in June last year, with Assad re-elected for a seven-year term with 88.7 percent of the vote.
It was dismissed as a "farce" by the opposition and its supporters, with voting held only in government-controlled areas and millions of the displaced and refugees unable to vote.
It is unclear whether new elections could be held under different circumstances, and Syria's opposition has dismissed holding a vote now as absurd.
"The Russians are ignoring the real facts on the ground, with millions who have been displaced inside and outside Syria, where cities are destroyed every day," said Samir Nashar of the Syrian National Coalition opposition group.
"What elections are they talking about holding under such circumstances?"
More than 250,000 people have been killed in the Syrian conflict which began with anti-government protests in March 2011 before spiralling into a multi-front war after a brutal regime crackdown.
Rebel forces were equally dismissive of Lavrov's offer Saturday of Russian support for "patriotic" opposition forces fighting against IS jihadists
Russia says its aerial campaign launched last month is targeting IS and other "terrorists" but moderate and Islamist rebels say they have been the real focus, not the jihadists.
Washington and Saudi Arabia, also insist Assad can have no role in the country's future, a position that Moscow and Damascus reject.
On Sunday, Saudi Foreign Minister Adel al-Jubeir said there had been "some progress so far and positions are coming closer" on a Syria solution.
But he said no agreement had been reached and reiterated "Bashar al-Assad will have no role in Syria's future".
- HRW urges Russia investigation -
On Friday, the US, Russian, Saudi and Turkish foreign ministers met to discuss Syria in Vienna but made no breakthrough. US Secretary of State John Kerry later said he hoped to convene a "broader" meeting as soon as October 30.
On the ground, Russia's strikes have allowed regime forces to launch several operations in provinces including northern Aleppo, where clashes continued on Sunday.
The Syrian Observatory for Human Rights said 43 regime forces and 28 IS fighters were killed in Aleppo in the last 48 hours, fighting for control of a key government supply route.
The monitor also reported that four opposition forces including a media activist were killed in clashes with regime forces in the north of Homs province.
Human Rights Watch on Sunday urged Russia to investigate two air strikes in the central province that killed 59 civilians.
The group said the strikes on October 15 were believed to be Russian and had killed at least 32 children.
The Israeli army said, meanwhile, that an Arab Israeli had crossed into neighbouring Syria using a paraglider, apparently intending to join opposition forces.
Some 45 Arab Israelis have joined jihadist forces in Syria, according to Israel's Shin Bet internal security agency.
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The visit by Russian lawmakers came days after Assad made a surprise trip to Moscow for talks with President Vladimir Putin.
That trip and ramped-up Russian diplomacy have led to speculation that Moscow is pushing for a new political agreement to end the conflict that began with protests against Assad's rule in March 2011.
But the shape of any such deal remains unclear, with Syria's opposition firmly against Moscow leading peace efforts while pursuing an air campaign it launched in support of Assad on September 30.
A Russian lawmaker said Sunday that Assad had expressed a willingness to hold new parliamentary and presidential elections, but only after Syria is "liberated" from Islamic State group jihadists.
"He is ready to conduct elections with the participation of all political forces who want Syria to prosper," the lawmaker Alexander Yushchenko told AFP.
Assad would run again "if the people are not against it," he added.
- Opposition dismisses new vote -
Russian Foreign Minister Sergei Lavrov has said that Syria needed to begin preparing for new elections.
Syria last held parliamentary polls in May 2012, with the next one planned for 2016.
A presidential election was held in June last year, with Assad re-elected for a seven-year term with 88.7 percent of the vote.
It was dismissed as a "farce" by the opposition and its supporters, with voting held only in government-controlled areas and millions of the displaced and refugees unable to vote.
It is unclear whether new elections could be held under different circumstances, and Syria's opposition has dismissed holding a vote now as absurd.
"The Russians are ignoring the real facts on the ground, with millions who have been displaced inside and outside Syria, where cities are destroyed every day," said Samir Nashar of the Syrian National Coalition opposition group.
"What elections are they talking about holding under such circumstances?"
More than 250,000 people have been killed in the Syrian conflict which began with anti-government protests in March 2011 before spiralling into a multi-front war after a brutal regime crackdown.
Rebel forces were equally dismissive of Lavrov's offer Saturday of Russian support for "patriotic" opposition forces fighting against IS jihadists
Russia says its aerial campaign launched last month is targeting IS and other "terrorists" but moderate and Islamist rebels say they have been the real focus, not the jihadists.
Washington and Saudi Arabia, also insist Assad can have no role in the country's future, a position that Moscow and Damascus reject.
On Sunday, Saudi Foreign Minister Adel al-Jubeir said there had been "some progress so far and positions are coming closer" on a Syria solution.
But he said no agreement had been reached and reiterated "Bashar al-Assad will have no role in Syria's future".
- HRW urges Russia investigation -
On Friday, the US, Russian, Saudi and Turkish foreign ministers met to discuss Syria in Vienna but made no breakthrough. US Secretary of State John Kerry later said he hoped to convene a "broader" meeting as soon as October 30.
On the ground, Russia's strikes have allowed regime forces to launch several operations in provinces including northern Aleppo, where clashes continued on Sunday.
The Syrian Observatory for Human Rights said 43 regime forces and 28 IS fighters were killed in Aleppo in the last 48 hours, fighting for control of a key government supply route.
The monitor also reported that four opposition forces including a media activist were killed in clashes with regime forces in the north of Homs province.
Human Rights Watch on Sunday urged Russia to investigate two air strikes in the central province that killed 59 civilians.
The group said the strikes on October 15 were believed to be Russian and had killed at least 32 children.
The Israeli army said, meanwhile, that an Arab Israeli had crossed into neighbouring Syria using a paraglider, apparently intending to join opposition forces.
Some 45 Arab Israelis have joined jihadist forces in Syria, according to Israel's Shin Bet internal security agency.
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