The twin offensives marked some of the most serious ground efforts against IS since the group declared its self-styled "caliphate" straddling the Syrian-Iraqi border in 2014.
Territory under IS control has been steadily shrinking for months but it has carried out a wave of attacks including bombings in the Syrian regime's coastal heartland Monday that killed 177 people.
It was the "deadliest bomb attack" on any regime-held area in Syria's five-year war, according to the Syrian Observatory for Human Rights monitoring group.
The offensive was aimed at pushing IS from the province's north and securing other areas, the alliance said in statement on Twitter.
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Baghdad-based US military spokesman Colonel Steve Warren confirmed the assault, saying it was "putting pressure on Raqa".
US air strikes would support thousands of SDF fighters, some of whom had been trained and equipped by American forces, he said.
If Raqa falls, "it's the beginning of the end of their caliphate," Warren said.
SDF spokesman Talal Sello said an assault on Raqa city "is not in our plan now".
Just before the SDF announcement, Russia said it would be ready to coordinate with both Washington and the SDF in an offensive for Raqa.
The US rejected a Russian proposal last week for joint air operations against jihadist groups in Syria.
The anti-IS coalition headed by Washington has set its sights on Raqa in Syria, as well as Fallujah -- and eventually IS's main bastion of Mosul -- in Iraq.
"It's clear that if the US wants to eliminate IS, it has to attack it on multiple fronts at the same time," said Washington-based Syria analyst Fabrice Balanche.