LONDON — As President Bush kicks off his second term, he has pockets of international support from Tokyo to Tel Aviv — but many around the world warily contemplate how the next chapter will unfold under a leader they see as cocky, shallow and dangerous.

They wonder: Will he now set his sights on Iran? Will he widen the rift with Europe? Or will he become more conciliatory, seeking to secure a legacy the world will ultimately respect?

There are some overseas supporters of Bush's foreign policy activism: pre-emptive strikes against perceived threats and the conviction that American muscle is a legitimate tool for spreading democracy. Israelis, for example, are grateful for his strong opposition to terrorism.

But the Iraq war has undermined his relationship with allies in Europe. And many here are offended by his unilateralist approach — carried out with a perceived cowboy swagger and accompanied by an overt religious fervor out of sync with Europe's secular politics.

There are even signs that unhappiness with Bush's policies and persona is spilling over into hostility toward Americans in general.

A BBC World Service opinion poll released Wednesday indicated majorities in seven important countries thought less of Americans because of Bush — led by Turkey with 72 percent, France 65 percent, Brazil 59 percent and Germany 56 percent.

On the other hand, some commentators have suggested second-term presidents can prefer world allies to domestic constituents, with an eye on a place in world history. Some optimistically look to Condoleezza Rice as a secretary of state with intellectual and international credentials, and a respected deputy in Robert Zoellick.

But mixed signals have been perceived from Bush's new team, too.

"Will George W. Bush turn more moderate or will he continue (an) aggressive foreign policy?" wondered the Austrian daily Die Presse. "The responses being sent out by Washington are varying: Soothing words for aggravated allies in Europe and threats against the 'outposts of tyranny.' "

The newspaper was referring to Rice's labeling of several nations, including Iran, Zimbabwe and North Korea, as "outposts of tyranny."

Across Europe, many vented their anxieties through Bush bashing.

A commentator in Croatia's Novi List daily quipped that as Bush was sworn in with the words "So help me God," the world might do well to "look up at the sky and say: 'God help us.' "