This journey will take him to Moscow on Friday, where he will meet Russian President Vladimir Putin and lobby to seek more to help end Syria's five-year-old conflict.
Last month, 51 State Department officials signed a memorandum criticizing the Obama administration's policy on Syria and urging US air strikes on Assad's forces.
Pentagon officials are pushing back against the Obama administration's plan to strengthen military cooperation between the United States and Russian Federation in the fight against terrorist groups in Syria.
Before leaving on Wednesday with Kerry for Paris, from where he was due to fly on to Moscow, the spokesman said "we're mindful of the clock".
"On Thursday late afternoon (July 14) President Putin will receive U.S. Secretary of State (John) Kerry and (Russian) Foreign Minister Sergei Lavrov".
Kerry will have to thread a needle. Syria's Air Force may conduct "air operations that are permitted as exemptions to the grounding of Syrian military aircraft".
Russian Federation and the United States are nominally co-chairs of worldwide efforts to bring Bashar al-Assad's regime to the negotiating table with armed opposition groups.
Much of Washington is wary about working too closely with Russian Federation.
But there has been little progress towards a resumption of political talks that was scheduled for August 1. All signs augur poorly for a breakthrough in a war that has killed as many as a half-million people since 2011, contributed to a global migration crisis and spawned IS' worldwide expansion. Fighting is intensifying near Aleppo, Syria's largest city, and Assad has reasserted control over areas of the country he once lost.
Syria is in the grip of what Kerry called the worst humanitarian crisis since World War II, and more than 4.8 million people have fled the country.
Some believe it may be the last attempt by the U.S to continue with its current plan in Syria. "So either something happens in these next few months or they are asking for a very different track".
However, he added, "While we have reached those overarching agreements, we have not seen the practical reality on the ground yet".
US officials say no agreement has yet been reached.
"We do this, and then what?" said a USA official, one of several who spoke on the condition of anonymity because they were not authorized to discuss the issue and feared identification as internal critics. "And we look to the Russians to make a greater use of the influence that we know that they have to make that happen", State Department spokesman John Kirby explained to reporters last week.
Washington has been criticised by some activists for moving too slowly to settle those fleeing the conflict, though Obama's opponents warn their number may include terrorists. "It's based on values", Assad said, according to Reuters. But the White House is facing major resistance to the idea from the USA military and those in the intelligence community who are working with local Syrian opposition forces-the very government officials who would carry out such a plan.
Russian Federation would be getting what it has wanted since intervening in Syria in late September: An global alliance of sorts. The U.S. initially sought to shut Russian Federation out of diplomatic discussions, but quickly reversed course and created the International Syria Support Group with Moscow's help.
Previously, Kerry has suggested that if there is no breakthrough by the target date then Washington might resort to an undefined "Plan B" to deal with Assad.
A cessation of hostilities deal was signed in February to stop nationwide violence in Syria. Several temporary and regional truces have followed, though none have ended the violence that has killed as many as a half-million people since 2011, contributed to a global migration crisis and spawned IS' worldwide expansion. Russian Federation has been keen to present its intervention as part of the global effort against IS and other extremist groups, and not as a ploy to keep Assad in power. But many in the US military are saying: no way.
The internal debate about how much to expand USA coordination with the Russians has exposed perhaps the greatest schism within the administration this year over the way ahead in Syria.
The Pentagon is concerned about such a scenario, according to the officials.
It's likely "the Russians will continue to bomb indiscriminately against forces opposed to Bashar al-Assad regardless of whether they are on the United Nations terrorism list", said Robert Ford, former US ambassador to Syria who is now a senior fellow at the Middle East Institute in Washington. If you would like to discuss another topic, look for a relevant article.
Be Civil - It's OK to have a difference in opinion but there's no need to be a jerk.