An umbrella group that fashions itself the head of Syria's political opposition should no longer be considered the "visible leader" of efforts to form a government to replace Bashar al-Assad, U.S. Secretary of State Hillary Clinton said Wednesday.

Clinton said the Syrian National Council, which is made up mostly of Syrian expatriates cannot alone shape the future of Syria apart from those fighting and dying inside the country amid a civil war that has claimed more than 30,000 lives.

"This cannot be an opposition represented by people who have many good attributes, but have in many instances not been in Syria for 20, 30 or 40 years," Clinton said during a joint news conference with Croatian President Ivo Josipovic in Zagreb. "There has to be a representation of those who are on the front lines fighting and dying today."

Her remarks come as preparations are underway for Arab League-sponsored meetings next week in Doha, Qatar, that will focus on the composition of a post-Assad political leadership in Syria.

"We have recommended names and organizations that we believe should be included in any leadership structure," Clinton said. "We've made it clear that the SNC can no longer be viewed as the visible leader of the opposition. They can be part of a larger opposition, but that opposition must include people inside Syria and others who have a legitimate voice that needs to be heard."

The SNC was formed last year after the once-peaceful uprising against al-Assad's rule turned deadly, but it garners little credibility from opposition forces inside Syria. While it was recognized as an interlocutor with the United States and other governments seeking a way to stanch the carnage of the al-Assad regime, the Obama administration has been frustrated by the lack of cohesion and infighting that seemed to define its workings. There are also questions of whether the group truly represented the interests of the wide variety of religious and ethnic groups inside Syria.

Clinton reiterated concerns that opposition forces are not doing enough to stem the tide of Islamic extremists who are exploiting the violent situation on the ground in Syria.

"We also need an opposition that will be on record strongly resisting efforts by extremists to hijack the Syrian revolution," she said. "There are disturbing reports of extremists going into Syria and attempting to take over what has been a legitimate revolution against a repressive regime for their own purposes."

As to a recent attempt by Lakhdar Brahimi, the U.N.-Arab League special envoy, to bridge a temporary cease-fire in Syria, Clinton said she was "not surprised" that it failed to take hold.

The Assad regime "did not suspend its use of advanced weaponry against the Syrian people for even one day," she said. "And the shelling in the suburbs of Damascus was as bad last weekend as at any time in the conflict."

Clinton is on a trip that already has included stops in Algeria, Bosnia-Herzegovina, Serbia and Kosovo. She is scheduled to visit with leaders in Albania before returning to Washington later this week.