The US is to help Yemen tighten security
After a two-hour meeting at a military air base next to Sanaa airport, President Ali Abdullah Saleh said he had agreed with Mr Cheney that "the fight against terrorism is paramount and should continue".
"We have increasingly developed close relations between ourselves and Yemen," said Mr Cheney.
Mr Saleh also called for "an intensive effort to end violence and press Israel to comply with international resolutions to end its aggression against the Palestinians".
Terror haven?
The US Government is considering sending military assistance to Yemen as part of its war on terrorism.
"In Yemen, we are working with the government to prevent al-Qaeda forces from regrouping there," Mr Cheney said in Egypt on Wednesday.
An adviser to the Yemeni Government, speaking on condition of anonymity, said the current plan was for at least three teams of 20-30 US military advisers to spend several months in Yemen.
Officials say that Yemen's remoteness and its history of terrorist activity make it a likely place for al-Qaeda to reconstitute its operation.
Groups of al-Qaeda sympathisers are thought to be living in the lawless tribal areas on the county's border with Saudi Arabia.
The US blames the al-Qaeda network - whose leader, Osama bin Laden, has family links to Yemen - for the attack on a US warship there in October 2000.
Yemen refused to help the subsequent investigation, but since 11 September the Yemeni president has sided with Washington.
He invited Dick Cheney to include the country in his Middle East tour after Yemeni officials arrested five men suspected of terrorist activity by the FBI and the country clamped down on hardline religious colleges feared to breed al-Qaeda style militancy.
Iraq
There has been persistent speculation that the US is planning to attack Iraq and Mr Cheney is touring the Middle East seeking Arab support for any strike against Baghdad.
After meeting Mr Cheney in the Red Sea resort of Sharm el-Sheik on Wednesday, Egyptian President Hosni Mubarak said his country would try to push Baghdad to allow UN weapons inspectors back into Iraq.
"I think, as far as my knowledge is, he's going to accept the inspectors," he told a press conference.
On the first leg of his tour, Mr Cheney met King Abdullah of Jordan, who warned that military action against Iraq could plunge the volatile region into turmoil.