A statement from the General People's Congress (GPC) late on Sunday refuted reports that Mr Saleh intended to leave for the UAE under pressure from Gulf and western countries to assist the transfer of power to the new president, Abdrabu Mansur Hadi.
As part of that transition, Mr Saleh would step down as head of the GPC, which is sharing power with opposition groups during the two-year changeover period, and allow Mr Hadi to govern unhindered.
As a result of this pressure, the party already authorised Abdulkareem Al Iryani to chair the meetings of the party leaders till a general meeting is held in which Mr Saleh will be officially removed from the leadership of the party.
But a western diplomat told The National that Mr Saleh changed his plans.
"He was willing to leave to the UAE but he later changed his mind, saying he did not get the visa," said the diplomat, on condition on anonymity.
According to the GPC party website, any plan by Mr Saleh to leave Yemen would contradict "commitments by national, regional and global parties" under the power-transfer plan.
Mr Hadi took over as the country's leader in February following nearly a year of street protests. Under a deal brokered by the Gulf Cooperation Council, Mr Saleh stepped down in return for immunity from prosecution for him and his aides. But Mr Saleh's network of family and friends in high-level security, military, and administrative positions has posed challenges to the new president.
In early April, Mr Hadi sacked Gen Mohammed Saleh Al Ahmer, Yemen's air force commander and a half-brother of Mr Saleh, along with 20 other officers and four governors loyal to the former president. The shake-up followed growing concerns that Mr Saleh was using the loyalists to further destabilise the country.
While almost all immediately left their posts, it took more than two weeks and the assistance of the UN special envoy, Jamal Benomar, to get the air force commander to step down.
Mr Benomar is also helping Mr Hadi to purge the Republican Guard forces, the country's best- trained soldiers, of Mr Saleh's family members who are refusing to follow Mr Hadi's orders. The envoy is said to have given Mr Saleh's relatives a deadline to obey, or the issue will be brought to a UN Security Council meeting set for May 17, according to an official who requested anonymity.
Yesterday, Mr Hadi made several key army appointments in an effort to assist Yemen's forces in their fight against Al Qaeda militants, who have taken over parts of the country's south. About 20 people were killed yesterday in an offensive against an Al Qaeda militant post in Lawdar, in Abyan province.
Military and local officials said 17 militants were killed while an army colonel and two civilian fighters died. The battle has been going on for three weeks after the militants launched an attack on the army in an attempt to seize the city.