The talks come after discussions between US secretary of state John Kerry and Russia’s foreign minister Sergei Lavrov on Saturday.
That meeting, held in Switzerland, lasted four and a half hours but ended without any clear result.
Mr Kerry said that those talks were “trying to find something that works other than military action” and that minsters offered suggestions that “really might be able to shape some different approaches”.
Today’s meeting includes Mr Kerry, Mr Johnson and their counterparts from France and Germany and is expected to see Mr Johnson proposing “no-bombing zones” for Syria – including Aleppo.
Mr Johnson has recently said it is time to consider “more kinetic options” including “military options”.
A report in the Sunday Times quoted a source close to Mr Johnson as saying he would seek backing from Washington and others for a proposal to threaten the Syrian military with strikes in retaliation for bombings of certain areas or facilities such as hospitals.
The talks come just hours after Turkish-backed rebels captured the symbolic northern Syrian town of Dabiq.
Dabiq has little strategic value but it is ideologically important to the Islamic State jihadists, who say it will be the site of a final battle between Christians and Muslims.
Turkey’s state-run Anadolu news agency said troops were now working to dismantle explosives laid by the retreating Islamic States troops.
Earlier on Sunday, Mr Kerry met with UN peace envoy Ismail Ould Cheikh Ahmed, Mr Johnson and their opposite numbers from Saudi Arabia and the UAE to discuss Yemen.
Speaking after the meeting, Mr Kerry called for the parties involve in that war to call a ceasefire within days.
He said: “We cannot emphasise enough today the urgency of ending the violence in Yemen.”
He added: “This is the time to implement a ceasefire unconditionally and then move to the negotiating table.”