Speaking after talks with British Prime Minister Tony Blair in London, Saleh acknowledged that the worsening security situation in Iraq was cause for concern but said his government needed to show it could impose order.
"At the end of the day, this is about the Iraqi leadership, this is about Iraqis assuming responsibility for their country," Saleh told reporters.
"We need the enduring support of the international community and the coalition but, ultimately, Iraqis have to be in the lead.
"I believe, come next year, you will be seeing Iraqi forces in the lead in many of the Iraqi provinces.
"By the end of the year, nearly seven or eight provinces of Iraq out of 18 provinces will be under direct Iraqi security control."
For his part, Blair said Britain intends to "hold its nerve" in Iraq, the BBC reported, amid increased pressure in London and Washington over their continued presence there.
The temperature rose further when Foreign Secretary Margaret Beckett, asked in a BBC radio interview if historians would judge Iraq to have been a "foreign policy disaster" for Britain, said: "Yes, they may. Then again, they may not."
Downing Street sought to play down her remarks and Beckett also said that troops would only be withdrawn from a democratic Iraq which could "cope" and was "back on its feet".
Opposition parties have called for lawmakers from Britain's lower House of Commons to be given a vote on whether to withdraw the country's 7,000-strong contingent.
But Blair's "continuing commitment to the cause of democracy, freedom and stability in Iraq" was a sign that Britain would not "cut and run" from the country, Saleh said.
With 86 deaths in the last three weeks, October remains on course to be the worst month for the US military since 2004, while the end of a bloody Muslim holy month of Ramazan saw fresh carnage on Monday.
In London, Saleh said he hoped the use of Iraqi troops, with British soldiers on stand-by, would become an increasing pattern.
Neither Blair's office nor Saleh commented on British newspaper reports on Monday that the British prime minister would pressure him to show that Iraqi security forces would be ready to take over in the south by next year.
Blair's official spokesman said it was up to the Iraqi government to judge when it was ready to take on that responsibility, describing the situation as "a process, not an event".
"We are not working to an arbitrary deadline. We are working to the point where the Iraqis are capable of providing for their own security. We are still in the process of Iraqisation," he added.
Saleh's meeting with Blair comes after US President George W. Bush met top advisors and generals at the weekend amid reports that he was ramping up pressure on Baghdad to control sectarian violence.
There were also suggestions that Washington could adjust its strategy if there was no improvement.
Saleh told British media in a round of interviews he understood the coalition's frustration at the slow pace of progress and the recent violence but called for patience.
A secure Iraq -- free from the "mortal, brutal threat of terrorism" that affected the whole Middle East -- was in the interest of the wider region, he told Sky News television later.
"The country is on the brink. I'm not saying it is not. The challenges are grave... We cannot afford to lose. We must win this battle and we will win it.
"But the rest of the world, the UK and the United States must understand that the stakes are high in Iraq.
"There is no option of cutting and running."

Copyright AFP (Agence France-Presse), 2006