A roadside bomb attack on an army vehicle killed six soldiers and wounded two near the North Sinai town of Sheikh Zuweid, a jihadist stronghold.
"An armoured personnel carrier for the army of the apostates was destroyed... killing and wounding all aboard," Ansar Beit al-Madqis said on a Twitter account attributed to it.
The military said six soldiers were killed in the attack.
"Their vehicle was targeted by an explosive device placed by the extremist terrorist elements which left an officer, a sergeant, and four soldiers martyred, and two other soldiers wounded," it said on its Facebook page.
Hours later a suicide car bomb targeting a police station in North Sinai's provincial capital of El-Arish killed eight people and wounded 45 others, health ministry spokesman Hossam Abdel Gaffar said.
The interior ministry said in a separate statement that five policemen and a civilian were among those killed in the police station bombing, while several policemen were wounded.
It said security forces fired at the vehicle before it was able to ram the police station.
A police officer said the truck was loaded with explosives but covered with straw, and blew up close to the police station.
"A den of the apostate police was targeted in El-Arish by a car bomb driven by a martyr," Ansar Beit al-Maqdis.
The group changed its name last year to the Sinai Province after pledging allegiance to IS.
It has claimed several sophisticated attacks in Sinai and the Nile valley and now wants to establish a province of the self-declared IS "caliphate".
- Attacks against crackdown -
Also on Sunday, an army captain and two soldiers were wounded in an attack on a checkpoint near the town of Rafah that borders the Palestinian Gaza Strip.
Ansar Beit al-Maqdis said one of its snipers shot at them.
The army has sent troops and armour to fight a dogged insurgency in the Sinai that has grown since then army chief and now President Abdel Fattah al-Sisi ousted his Islamist predecessor Morsi.
Ansar Beit al-Maqdis says attacks on the security forces are in retaliation for a government crackdown on Morsi's supporters that has left hundreds dead.
Thousands more have been imprisoned and dozens sentenced to death.
Jihadist attacks in Sinai have left scores of security personnel dead.
On April 2, Ansar Beit al-Maqdis militants launched simultaneous attacks on five checkpoints in the region that killed 15 soldiers and two civilians.
In January, a combined rocket and car bomb attack on a military base, a nearby police headquarters and a residential complex for army and police officers killed at least 24 people, most of them soldiers.
The attacks came despite stringent security measures imposed by the army in the province.
After a late October attack on a military base near El-Arish, the army imposed a night-time curfew and state of emergency in parts of the region.
The army has also built a buffer zone along the border with the Gaza Strip to prevent militants infiltrating from Palestinian territory using illegal underground tunnels.
On Sunday, Sisi issued a decree making the digging or use of such illegal tunnels in border areas punishable by life in jail.
The army says hundreds of underground tunnels connecting the peninsula to the Gaza Strip have been destroyed since Morsi's ouster.
Egypt is also facing a threat on its western border from a chaotic Libya where the influence of IS -- which has seized chunks of Syria and Iraq -- is growing.
Arab leaders agreed at a summit in March to form a joint military force to fight "terrorist groups" in the region, after Sisi insisted on the creation of such a force to contain IS.
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