Speaking at an exclusive interview with The Observer, Bush said that the US and Britain want to withdraw troops from Iraq but this should be "based on success" and not a "definitive timetable".
"I am confident that he, like me, will listen to our commanders to make sure that the sacrifices that have gone forward won't be unraveled by drawdowns that may not be warranted at this point in time. I look forward to discussing it with him," said Bush.
At a joint news conference with Bush following a meeting with him at No. 10 Downing Street, Brown showed his support to Bush by declaring that there is no "timetable" for the withdrawal of British troops from Iraq.
"In Iraq, there is a job to be done and we will continue to do the job and there will be no artificial timetable," Brown said.
"We are making progress with training and with elections ... We are moving from combat to overseeing," Brown said.
Meanwhile, President Bush emphasized that troop withdrawal would depend upon success in Iraq.
"We are withdrawing troops from Iraq ... The plan is to bring them home based on success," he said, "We make our decisions in Iraq without an artificial timetable set by politics."
Dismissing reports on differences with Brown over Iraq, Bush said, "I have no problem with how Gordon Brown is dealing with Iraq."
"He's been a good partner," he added.
Bush secures support in Afghanistan
Although US troops, British and other troops have been still fighting a fierce Taliban insurgency for seven years, the security in Afghanistan is deteriorating.
In a keynote speech at the Paris-based Organization for Economic Cooperation and Development (OECD) last Friday, Bush said that Europe must do more to help Afghanistan overcome ongoing deadly violence.
"Our nations must ensure that Afghanistan is never again a safe haven for terror," Bush said.
Speaking after talks with Bush on Monday, Brown announced that Britain will send "additional troops" to the violence-wracked Afghanistan, "bringing our numbers in Afghanistan to the highest level".
"We have resolved, first of all, as we did some years ago, that it is in the British national interest to confront the Taliban in Afghanistan or Afghanistan would come to us." said Brown.
Later, British Defense Secretary Des Browne said in the parliament that 230 more troops would be sent to Afghanistan by spring 2009, taking the number of the troops there to 8,030.
The announcement came as the number of British soldiers killed in Afghanistan since 2001 reached 102. And Brown praised Bush for his "steadfastness and resoluteness" in rooting out terrorism all over the world, calling him "a true friend of Britain."
British decision would strongly back Bush's global war on terror.