Senior US officials have singled out Iran for criticism, a day after giving a progress report on security in Iraq.
Ambassador Crocker and Gen Petraeus have testified to Congress
Gen David Petraeus, top US commander in Iraq, and US envoy to Baghdad Ryan Crocker both cited evidence of Iranian involvement in attacks on US troops.
Responding to their report, Secretary of State Condoleezza Rice said it made clear Iraq's security had improved, but Iran was a "troublesome neighbour".
US President George W Bush is due to address the nation on Thursday evening.
His speech will follow criticism from senior Democrats, who have said proposed reductions in US troop numbers in Iraq are "insufficient" and do not represent a change in course.
Mr Bush is expected to announce that he plans to reduce US troops in Iraq by about 30,000 by next summer, if certain conditions are met, White House officials say.
The move would bring the number of US troops in Iraq to "pre-surge" levels, with about 130,000 still deployed in Iraq.
Gen Petraeus endorsed a gradual reduction in troop numbers in his testimony to Congress on Monday and Tuesday, saying the surge was working, but warned against premature withdrawal.
Speaking to reporters, Gen Petraeus said there was "very clear" evidence of Iranian involvement in attacks on US forces in Iraq.
Mr Crocker echoed the message in an interview with the BBC's John Simpson, saying the role of Iran in undermining security in Iraq was "pretty well established".
"We have seen a serious Iranian effort to exercise malign influence through extremist militias," he said.
"And we know it because we've captured leaders of some of these secret organisations... and they've been very clear about their Iranian connections."
Asked how the US should handle Tehran, Mr Crocker said the administration viewed Iran as an international issue that should be dealt with by diplomatic means, such as the UN Security Council.
Iran has denied claims it has been involved in arming and training militias opposed to US forces in Iraq.
Speaking to the US TV network NBC, Ms Rice gave the first reaction by the Bush administration to the progress report by Gen Petraeus and Mr Crocker.
Mr Bush (right) will endorse Gen Petraeus' proposals, officials say
She said that while the Iraqi government must do more on national reconciliation, the security gains made in Anbar province and some Baghdad neighbourhoods were significant.
Once the security gains were solidified, the US would begin to draw down American forces and hand over responsibility to the Iraqis, she said.
However, she warned against leaving prematurely, pointing out that Iran's President Mahmoud Ahmadinejad had said his country was "prepared to fill the vacuum" if the US left.
The message that security has improved is clearly what the Bush administration intends to highlight from Gen Petraeus's and Mr Crocker's testimony, the BBC's Jonathan Beale in Washington says.
President Bush will give a 15-minute speech setting out his policy on Thursday night at 2100 local time (0100GMT on Friday).
'More of the same'
Meanwhile, Senate Democratic leaders rejected the call for a reduction in US troop numbers of up to 30,000 by next July as too small a step.
Senior Democrats have said it is time for a change of course in Iraq
Senate Majority Leader Harry Reid said Gen Petraeus's recommendation was "neither a drawdown or a change in mission that we need.
"His plan is just more of the same."
He called on Senate Republicans to stop walking "lockstep" with the president over Iraq, saying the Democrats would offer alternatives when the Senate discusses a defence bill next week.
The Democrats have so far been unable to pass legislation to set a timetable for withdrawal from Iraq because their majority in Congress is too slim to overturn a presidential veto.
Democratic Senator Carl Levin, chairman of the Senate Armed Services Committee, said it appeared that President Bush was prepared to "stay the course indefinitely".
A record 168,000 US troops are now in Iraq after 30,000 arrived in the surge between February and June.