Prime Minister Abdullah Badawi would not confirm he would be a candidate.
Ministers in government and analysts said this allowed for the possibility of a faster handover of power by Mr Abdullah to his deputy.
The prime minister has been under increasing pressure to resign in the face of a revived opposition.
Ever since he led his government to an abysmal showing at the election Mr Abdullah has been battling to stay at the helm of Malaysia's ruling Barisan Nasional or National Front coalition.
He resisted pressure to resign in the immediate aftermath of the result in March this year, and then hammered out a plan for a transition of power to deputy prime minister Najib Razak in 2010.
UMNO's latest decision to delay its leadership contest is seen as significant because traditionally, the UMNO president becomes the country's prime minister.
Reporters said Mr Abdullah's refusal to say if he would be a candidate for leadership six months from now heightens the political instability.
"I have not made any decision as far as this particular point is concerned," Mr Abdullah said.
"The decision is mine, you can go on guessing. As far as I'm concerned I love the party," he added.
Growing discontent
But the opposition has been threatening to topple the government, and the discontent within his own party has been growing, the BBC's correspondent Robin Brant says.
Mr Abdullah's plan to hang on until next June now looks unlikely, and it seems almost certain that these are the final months of his premiership, our correspondent says.
He says the message from Mr Abdullah's allies in UMNO is clear - we are giving you six months, then you should go.
Mr Abdullah admitted that several members of UMNO's supreme council were pushing him to quit and said the party polls had been postponed "to help facilitate an early transition".
"Since we have decided to speed up the transition, the original 2010 deadline is out of the question," he said.
Trade Minister Muhyiddin Yassin, one of those pushing for a revamped leadership, also indicated that the 2010 handover plan was now abandoned.
"As far as I'm concerned it's a new deadline that has been set. In a way it is to bring forward the deadline," he told reporters.
Mr Najib is widely expected to replace Mr Abdullah, at a time when the government is the most unpopular it has been in half a century.
Mandate 'lost'
Leading the opposition Pakatan Rakyat alliance is former deputy prime minister Anwar Ibrahim. In Hong Kong to attend a private bankers' conference, he said that the possible accession of Mr Najib to power would only strengthen opposition to the government.
"The issue is not whether Prime Minister Abdullah leaves or his deputy takes over. The issue is that they have lost their mandate from the people," Mr Anwar said.
"However unpopular Abdullah is now, Najib is more unpopular than Abdullah... Najib has a major problem, in credibility," Mr Anwar said.
He said there were many unexplained issues ranging from a past murder case, and alleged kickbacks on military procurement deals, which Mr Najib should help explain.
"Because of our moral position, in terms of our agenda for change and reform, for transparency and accountability, you can see of course a much stronger base," Mr Anwar said of his opposition alliance.
"It affirms our case. It's not we're talking about individuals, we're talking about systemic change. We need reform in the country," he said.
Mr Anwar claims to have a majority of members of parliament backing his bid to topple the government and has been pressing the government to call a vote of no-confidence to prove it.
The government lost its two-thirds majority in parliament at general elections in March this year, for the first time since Malaysian independence.
