The new interim Iraqi government says it is considering Jordan's offer to send troops to help stabilise Iraq.
Jordan's offer was the first from an Arab country
However Iraq's Deputy Foreign Minister Hamid al-Bayati told the BBC the proposal by King Abdullah was likely to be rejected.
He said Iraq's Prime Minister Ayad Allawi had written to Egypt, Bahrain and Oman requesting soldiers be sent to Iraq to help restore security.
Yemen has also said it would send troops under certain conditions.
Mr Bayati said Iraq would be unlikely to accept troops from countries on its border because of concerns that they have interests in Iraq which could, as he put it, complicate the security situation.
COALITION TROOPS IN IRAQ
The Netherlands (1,400)
South Korea (600)
An Iraqi interior ministry spokesman, Saba Khaddam, told the BBC Jordan's offer "will have to be discussed in detail as to the nature of the help, the length of it, its fundings... How it can be implemented and whether or not it should be part of the multinational forces".
The BBC's Dan Damon in Baghdad says the problem with accepting Jordan's offer would be that Turkey could then ask to send some of its troops.
Kurds in the north, who have fought the Turkish army in occasional cross-border skirmishes for years, would be extremely apprehensive about that, he says.
Yemen said it was ready to send troops to take the place of coalition forces, if the United Nations and the Arab League took control of security.
'Difficult to say no'
Jordan's King Abdullah made his proposal in an interview with the BBC's Newsnight programme.
"If the Iraqis ask us for help directly it will be very difficult for us to say no," he said.
"If we don't stand with them, if they fail, then we will pay the price.
1990-91- Jordan remains ally despite Iraq invasion of Kuwait
1995 - Saddam Hussein's sons-in-law defect to Jordan; join opposition, before returning to Iraq where they are killed
1998 - killing of Iraqi diplomats and businessmen in Amman
2003 - Prince Hassan attends Iraqi opposition conference
2003 March - US forces covertly use Jordanian bases during war to oust Saddam
2003 August - Bomb attack on Jordanian embassy
"My message to the president and prime minister is 'tell us what you want, tell us how we can help and we have 110% support for this," he said.
The king is the first Arab leader to consider sending troops to Iraq and the move is likely to please the US.
"To have fellow Arabs patrolling I'm sure would be welcome," an unnamed US official told Reuters.
Jordanian Foreign Minister Marwan Moasher played down the king's remarks, saying they were meant as an expression of support.
"We have no intention of sending troops at this time. [King Abdullah's] statement is a statement of support for the Iraqi government rather than an announcement of sending troops," he told AFP news agency.