"There are still political steps that must be taken and Iraqis must use the political process to resolve their remaining differences and advance their national interest and we stand ready if asked, and if helpful to help in that process."
A senior US official told reporters that Biden had also threatened that Washington would disengage politically if violence in Iraq spiked.
"If it actually reverts to violence then that would change the nature of our engagement. He was quite direct about that," the official told reporters.
"He also said if by the actions of different parties in Iraq, Iraq were to revert to sectarian violence or engage in ethnic violence then that's not something that would make it likely that we would remain engaged."
Biden said: "In recent days the enemies of Iraq have once again tried to reignite sectarian violence through several deadly bombings.
"They will fail, they will fail because Iraq's future belongs to those who are attempting to build Iraq, not those who are attempting to destroy it."
Maliki said: "I have seen very clearly the keen determination from the vice president and his administration to support Iraq on a political level and in the democratic area and a great readiness to give us or to lend anywhere we ask a lending hand and support.
"In respect to the sovereignty of both countries we are looking also for ways for exchange that support the interests of both parties."
A fiery protest marked the start of Biden's visit to Iraq, with supporters of the Shiite anti-American cleric Moqtada al-Sadr burning the Stars and Stripes.
Biden met General Ray Odierno, the top US officer in Iraq, and Christopher Hill, Washington's ambassador in Baghdad, who briefed him on the military and political situation, three days after a major US troop pullback.
The vice president's trip, aimed at bridging Iraq's sectarian divide ahead of a complete American military pullout by 2011, comes just after President Barack Obama charged Biden with overseeing the US departure.
Biden had breakfast with his son Beau, an army captain in Iraq, before meeting Odierno with whom he discussed "the capabilities of Iraqi forces and the mission of US forces going forward," according to the White House.
A stark reminder of the legacy inherited by Obama's administration, however, came in Sadr City, where hundreds of supporters of Sadr, who is in self-imposed exile, chanted anti-US slogans.
"No, no America, no, no occupation. Yes, yes Iraq," they shouted as a US flag was reduced to ashes in the sprawling Baghdad Shiite district.
Biden, who landed late on Thursday, also visited American troops, who are now stationed on the outskirts of Iraqi cities following a June 30 withdrawal from urban centres.
It is Biden's first trip to Iraq since he was sworn in as vice president in January, but he previously made several visits when he was chairman of the Senate foreign relations committee.
The White House said Biden would work closely with Odierno and Hill, as US forces prepare to leave the country for good, ending a military engagement that started with the 2003 invasion ordered by Obama's predecessor, George W. Bush.
The vice president's arrival in Baghdad was welcomed by Wathad Shaqir, chief of the Iraqi parliament's national reconciliation committee.
"I believe he has brought some suggestions regarding the reconciliation project," Shaqir told state television, noting he was happy that Biden's communal federation idea had been abandoned.
A key problem facing the reconciliation effort is a Sunni demand that Baathists loyal to now executed dictator Saddam Hussein, who were excluded from politics after the US-led invasion six years ago, be reintegrated.
Major difficulties are also posed by the crucial oil-hub city of Kirkuk, which Iraq's autonomous Kurdish region has laid claim to in a new draft constitution that has irked the central government in Baghdad.
The Kurds have long striven to expand their northern territory beyond its current three provinces to other areas where the population was historically Kurdish.
Kurdistan, with its capital in Arbil in northern Iraq, has its own flag which is raised beside the federal flag, and also has its own slogan, national anthem and national day.
Iraq marked Tuesday's American pullback with a national holiday.
The country's 500,000 police and 250,000 soldiers are now in charge in cities, towns and villages. Most of the 133,000 US troops, now based outside of cities, will largely play a training and support role.
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