CAIRO, May 30 (Reuters) - Egyptian authorities have arrested a first suspect in connection with the kidnapping of seven security men two weeks ago by Islamist militants in Sinai, security sources said on Thursday.

The desert along Egypt's border with Israel has slipped into anarchy since President Hosni Mubarak was toppled in a popular uprising in 2011 and the state has struggled to restore order there since.

The militants, who demanded the release of jailed Islamists, let the men go on May 22 after mediation by Bedouin tribal leaders.

Prior to their release, Egypt stepped up the security presence in North Sinai, setting up new roadblocks and reinforcing existing ones with the aim of choking off supplies and reinforcements for the kidnappers.

Waleed Saleh el-Nekhlawy, 23, was being held in police custody being investigated for his suspected role in the kidnapping and uploading a video of the men while they were in captivity, one source said.

The kidnappers have been identified by the government as members of Tawhid wal Jihad, a hardline group of Islamists, who have been blamed for bomb attacks on Sinai tourist resorts from 2004 to 2006.

They had demanded the release of six Islamists sentenced to death last September for attacking a police station in North Sinai in 2011, killing seven people.

The militants have launched attacks on Israel and targets in North Sinai, where security problems have been exacerbated by a flow of weaponry smuggled from Libya. An Israeli defence official, speaking after the release of the seven, said it was vital that Egypt succeed in crushing terrorism.

Sinai's militancy problem predates the 2011 uprising and has grown partly out of state neglect and heavy-handed security crackdowns in the past. (Reporting Youssry Ahmad; Writing by Asma Alsharif; Editing by Alison Williams)