Mr Sherif had only been in Iraq for five weeks before he was kidnapped
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A message posted on the internet says the abduction of the Egyptian envoy in Baghdad was carried out by a group calling itself al-Qaeda in Iraq.
The statement purporting to be from the militant group, which is led by Abu Musab al-Zarqawi, is the first claim of responsibility for the kidnapping.
Ambassador Ihab al-Sherif was seized on Saturday while buying a newspaper.
Two other diplomats from Muslim countries survived separate attacks in Baghdad on Tuesday.
Pakistan's envoy escaped unhurt but Bahrain's envoy was shot in the arm.
Separately, in an audiotape broadcast on the internet, Zarqawi is heard declaring war on the Iraqi army "of apostates and mercenaries".
The voice, which is similar that in previous webcasts said by US officials to be the Jordanian-born militant, lashes out at contacts between some insurgents and US officials.
"The enemy is experiencing its worst days on the earth of Mesopotamia," the voice says.
Appeals
"The Egyptian ambassador has been kidnapped by our mujahideen and he is under their control," said the Sherif kidnap claim, which was not accompanied by photographs.
It promised to release more details as they "became available".
No demands were made in the message, posted on a web forum, and nothing was said about the kidnappers' plans.
The family of Mr Sherif, whose country is the main US ally in the Arabic world, has pleaded for his safe return.
Cairo has appealed to the kidnappers to treat him well and view him as an Arab patriot and both Egyptian and Iraqi diplomats are working to free him.
Ties with Egypt
Correspondents say the kidnappers may have been angered by Egypt's decision to designate Mr Sherif an ambassador, following his arrival in Iraq five weeks ago.
The move made Egypt the first Arab country to upgrade ties with Iraq.
The US has been encouraging Arab countries to appoint ambassadors to Baghdad in an attempt to strengthen the new state and undermine the insurgency.
Many withdrew their ambassadors after Saddam Hussein invaded Kuwait in 1990.
Last July, militants briefly kidnapped Egyptian diplomat Mohamed Mamdouh Qutb.
Al-Qaeda in Iraq has claimed responsibility for many of the biggest attacks of the insurgency, and the execution-style killing of hostages.
Its leader has a US bounty of $25m on his head.