Syria says it will ask Baghdad for evidence of foreign fighters crossing its borders adding that it wants to open a "new page" with Iraq.
Mr Shara says Syria wants to check the accuracy of the claims
Foreign Minister Farouq al-Shara also says Damascus hoped to reopen its embassy in Baghdad "very soon".
Washington has frequently accused Syria of allowing militants to cross into Iraq to join the insurgency there.
US Secretary of State Condoleezza Rice repeated the warning on Thursday, calling for less words and more action.
"This is a government that can take action on its border to prevent these cross-border activities which are really contributing dramatically to insecurity in Iraq," she said after a meeting of G8 foreign ministers in London.
"So, if they are prepared to do it, they should just do it."
Mr Shara told reporters Syria wanted evidence of Washington's claims of cross-border activity.
"We will be contacting officials in Baghdad very soon to know the source and truth of these allegations," he said, adding that they would ask for documents and evidence.
He said Syria was "ready to co-operate and open a new page with Iraq".
"But we are not ready to hear every now and then accusations that may not have a basis of truth," he added.
"We want to confirm by words and deeds how accurate these accusations are and what solutions could be found."
He told reporters Syria hoped to send a delegation soon to Baghdad soon to discuss re-opening its embassy there.
US and Iraqi forces carried out a major offensive against militants in western Iraq's restive Anbar province, on the border with Syria, last week.
The US military said it had killed 50 rebels and arrested 100 others during Operation Spear.