"We are not interested in turning away from anyone. We are ready to resume normal, full-fledged relations with the European Union, with the United States, but only on an equal basis," Lavrov said.
Western countries have a lot of work to do to restore Russia's trust,he added.
"Our Western partners must do a lot to restore the Russian Federation's trust in them, to restore the predictability in European affairs," Lavrov said, Sputnik reported.
Ties between Russia and the West suffered a severe blow after Crimea became part of Russia in 2014.
The West has imposed political and economic sanctions on Moscow over annexation of Crimea and Russia's alleged meddling in the Ukrainian conflict.
The Kremlin has repeatedly refuted the accusations and introduced countermeasures, banning a list of EU products.
The United States is shying away from talks with Russia on cybersecurity issues, Lavrov said.
"A year ago, through the prosecutor general's office, we offered the United States to hold talks on cooperation in the cybersecurity field," Lavrov said.
"In November last year, we suggested holding serious expert talks. There was no response. In January this year, I reminded [US Secretary of State] John Kerry that we would like to receive some sort of answer… I reminded him in May, and I reminded him now, when we held a meeting on Syria in Geneva a week ago. He was surprised that there had been no response yet. Meanwhile, the US Department of Justice, where the request was sent, has refused to send a written response to our direct reminder," he added.
The West has no legal obstacles when it comes to recognizing the reunification of Crimea and Russia, but it chooses to use this issue for its own political goals, the Russian diplomat said.
"There are no legal obstacles hindering our Western partners from recognizing Crimea becoming part of the Russian Federation. There is no political will, but a political wish to use this situation as part of a political line that was carried out under US leadership for a long time, long before Ukraine; a line to contain Russia," Lavrov said.