The Al-Watan newspaper said Kerry's comments, in an interview recorded on Saturday, also "open the door to a new stage in political negotiations."
The top US diplomat made headlines by saying negotiations with Assad's regime were necessary to end the bloody conflict now in its fifth year.
"Well, we have to negotiate in the end," he said, when asked by CBS television if he would negotiate with the Syrian leader.
Kerry's spokeswoman later stressed that the comments indicated no change in US policy, saying "there is no future for a brutal dictator like Assad in Syria."
But Syrian state television immediately flashed his comments as breaking news when they emerged on Sunday, and other media touted the remarks as a U-turn by the US administration.
"Facing a fait accompli, the American administration has backed down and recognised the need to reposition its policy on the Syria crisis," wrote Al-Watan, which is close to the government.
Washington recognises the need to put its Syria policy "back on the right track by negotiating with President Assad to solve the conflict," it added.
It said Kerry's comments underlined the "failure" of US policy towards Syria and were an acknowledgement that Assad will not be ousted militarily.
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"This is a new recognition of President Assad's legitimacy, his key role and his popularity, and the resulting necessity of negotiating with him," the daily said.
It suggested that Kerry's comments could "open the door to a new stage in political negotiations," with Washington perhaps dispatching a representative to talks being hosted by Moscow on April 6.
Moscow, a key Assad ally, is seeking to sponsor its own peace initiative in Syria, but there has been no indication yet of whether the US-backed Syrian opposition will attend the talks.
The Al-Baath newspaper, mouthpiece of Assad's ruling Baath party, said Kerry's comments "confirmed once more the failure of the American-Zionist project against Syria."
"The West has begun to fear the terrorism it cultivated," the daily said.
Syrian state media make no distinction between Western-backed rebels battling to oust the regime and jihadist fighters like those of the Islamic State group.
While Kerry's remarks made a splash, there was some scepticism in the state press about whether they signalled a real intent to negotiate with Assad.
Al-Thawra questioned whether the comments were "a recognition (of Assad's importance) or a tactic?"