"It is not our design or desire that we see a Russia isolated through its own actions," Kerry said at the start of the two-day meeting.
"Moscow could rebuild trust and relationships if it simply helps to calm turbulent waters," he said.
"The United States and countries that support Ukraine's sovereignty and rights do not seek confrontation".
Diplomats at the meeting called for a renewed effort to implement a truce brokered by Russia on September 5 that has been frequently broken, sending the death toll from the conflict soaring to 4,300.
Swiss President and acting OSCE chair Didier Burkhalter said the conflict in Ukraine had fuelled a broader crisis of European security, with a surge in military activity by Russia — whose aircraft have made several forays into NATO airspace — sparking increasing unease.
"Security has deteriorated markedly in Europe. Trust between Russia and the West has eroded. We have seen a dangerous increase in military activity and belligerent rhetoric lately," he said.
German Foreign Minister Frank-Walter Steinmeier warned that the conflict had raised the spectre of "a new division of Europe."
"We have not advanced as much as we would like in defusing this crisis," he told journalists.
"The danger of a new escalation cannot be ruled out."
With East-West relations at frosty levels not seen since the Cold War, Russia's decision this week to cancel a project to build a massive gas pipeline that would bypass Ukraine and deliver energy directly to southeastern Europe further complicated ties.
European Commission chief Jean-Claude Juncker said on Thursday that Russia was now a "strategic problem" for the EU, which would not accept "blackmailing on energy matters."
An elusive ceasefire
Meanwhile, a lasting ceasefire remained elusive in eastern Ukraine.
Since the Minsk deal, fighting has continued around the flashpoint Donetsk airport and a fresh truce agreed there appeared to have crumbled Wednesday just hours after it was signed.
A separate truce planned for the Lugansk area Friday was also shrouded in uncertainty as rebel leaders have complained about the terms.
Heavy rocket fire rang out throughout the night in Donetsk, an AFP reporter said, and the Ukrainian army on Thursday reported more than 70 rebel attacks on its positions in the past 24 hours.
"It is not a Ukrainian crisis, it is not an OSCE crisis, it is about Russian aggression," said Ukrainian Foreign Minister Pavlo Klimkin in Basel.
Kerry, who met his Russian counterpart Sergei Lavrov on the sidelines of the OSCE conference, accused Moscow of torpedoing the deal it had brokered by continuing to support rebels in eastern Ukraine.
"Russia continues to supply new weapons and increase support for armed separatists" and thus is failing "to live up to an agreement that it actually negotiated and signed".
European Union foreign policy chief Federica Mogherini, who also held talks with Lavrov, urged Russia to withdraw from Ukraine.
Putin says sanctions 'a pretext'
US President Barack Obama said Moscow was unlikely to shift its stance until the reality of sanctions, which were "having a big bite" on its economy, sunk in.
In Moscow, Putin lashed out at the West for using the Ukraine conflict as a pretext to restrain a muscular Russia with sanctions.
"Every time someone believes Russia has become too strong, independent, these instruments get applied immediately," he said, referring to the sanctions that have pushed the country towards recession coupled with falling oil prices.
However, Putin said in his state of the nation address he would not sever ties with the West despite the confrontations with Brussels and Washington.
In Basel he received backing from ally Belarus, whose Foreign Minister Vladimir Makei slammed the West for "double standards" in the Ukraine crisis.
"We have come close to a dangerous line," he warned.
During the year that Switzerland has headed the OSCE, the organization has seen its standing swell in step with the deepening Ukraine crisis.
In its biggest operation ever, it currently has some 500 people on the ground monitoring the tattered September truce.