Clinton was interviewed from Iraq alongside Republican Senator John McCain, who said Jaafari appeared likely to become the next premier.
“I think we know that he is probably going to be the prime minister,” McCain told NBC’s “Meet the Press.”
Clinton, a New York Democrat and former first lady, added: “There are grounds both for concern and for … vigilance about this.”
“But, again, I am willing to look at the situation and … not yet jump to any conclusions,” said Clinton, who is considered a possible 2008 presidential candidate.
“It is a historical fact that he along with the Dawa party have had connections with Iran,” partly because of their common opposition to former Iraqi leader Saddam Hussein, Clinton said.
“But I don’t believe there is by any means a large body of opinion that wants to cede independence and control over Iraq’s future to Iran,” Clinton said.
“Having said that, I think we have to watch this very closely,” she added. “There are obviously areas of influence, there is a temptation on the part of the Iranians to try to fund … their own interests on this side of the border.”