Asked by reporters to confirm whether the issue would be raised, Hadley said: "I think you're going to find that prime minister Maliki is going to bring that up with the president."
The White House acknowledged on Monday that sectarian violence in Iraq had entered "a new phase" but denied it amounted to civil war.
Hadley, who is accompanying Bush to the Estonian capital, Tallinn, said: "We're clearly in a new phase, characterised by this increasing sectarian violence that requires us obviously to adapt to that new phase and these two leaders need to be talking about how to do that."
"The Iraqis don't talk of it as a civil war"
Stephen Hadley, the US national security adviser
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Kofi Annan, the UN secretary-general, said earlier on Monday that Iraq was close to civil war. "In fact we are almost there," the UN chief said.
However, Hadley said: "The Iraqis don't talk of it as a civil war," arguing that the police and army had not fractured on sectarian lines and the Iraqi unity government was holding together.
Bush is in Europe for a summit with Nato allies in the Latvian capital, Riga, on Tuesday and Wednesday.
Hadley said Bush had telephoned Hosni Mubarak, the Egyptian president, and discussed the importance of supporting the Lebanese government and of "sending a firm message to Syria that it needs to stop destabilising that government".
Many Lebanese blame Damascus for the assassination last week of Pierre Gemayel, a Lebanese cabinet minister, the latest in a series of murders of anti-Syrian politicians since Syria was forced to withdraw its troops from Lebanon last year.