Story highlights Russia's Vladimir Putin says he wants to see the "successful development" of the relationship

He says U.S.-Russia relations should be based on mutual respect and understanding

Ukraine crisis has heightened tensions between Russia and the United States

Russian President Vladimir Putin said Friday he hoped for better ties with the United States in a July Fourth message to his U.S. counterpart, Barack Obama.

The Independence Day wishes come at a time when relations between the two nations are at their lowest ebb since the Cold War, fueled by tensions over Russia's actions in Ukraine.

According to the Kremlin website, Putin "expressed a hope for the successful development of the relationship between both countries, based on equal rights and utilitarianism, despite all the difficulties and disagreements they are facing at the moment."

Putin also said that since the two nations are responsible for global security, they "should cooperate in the interests of not just their own people, but the entire world."

He urged the building of a bilateral relationship based on "mutual respect" and understanding of each other's interests.

Moscow has repeatedly complained that the West has not taken its legitimate interests in Ukraine into consideration or treated it as an equal partner.

JUST WATCHED Poroshenko says he's ready for peace deal Replay More Videos ... MUST WATCH Poroshenko says he's ready for peace deal 12:06

JUST WATCHED Clinton: I made a connection with Putin Replay More Videos ... MUST WATCH Clinton: I made a connection with Putin 03:10

JUST WATCHED Putin, Obama face to face in France Replay More Videos ... MUST WATCH Putin, Obama face to face in France 03:04

The White House gave a muted response to Putin's gesture.

"We've seen the message but have no particular comment," said National Security Council spokeswoman Caitlin Hayden.

The United States and European Union have imposed targeted economic sanctions on Russian individuals and companies in response to Moscow's actions in Ukraine.

Russia annexed Ukraine's Crimea region in March despite condemnation from the West. Its amassing of troops along the border with Ukraine has led to heightened tensions.

The EU and the United States have repeatedly warned Moscow that more economic sanctions could be imposed if it doesn't act to defuse the crisis.

In a bid to end the pro-Russia separatist unrest roiling the east of his country, Ukraine's new President Petro Poroshenko has proposed a peace plan that calls for the rebels to lay down their arms and engage in talks. He also urged the strengthening of Ukraine-Russia border controls, the freeing of hostages and changes to the Ukrainian Constitution to decentralize power.

NATO chief Anders Fogh Rasmussen urged Moscow last week "to create conditions for the implementation of the peace plan, to end its support for separatist troops, and to stop the flow of weapons and fighters across its border."