The US and Russia have agreed to extend an arms control treaty limiting their deployed nuclear warheads after Joe Biden’s first phone call as president with Vladimir Putin.

At the same time, Biden took a firm position on Russian actions that Donald Trump largely ignored, raising concerns about the poisoning and arrest of the opposition leader, Alexei Navalny, warning Putin that the US supported Ukraine against Russian “aggression”, complaining about Russian interference in last year’s US presidential election, and the “Solar Winds” cyber-attack on US government agencies last year.

Biden challenged Putin on US intelligence reports that Russia had offered bounties to the Taliban and other extremist groups in Afghanistan for the killing of US soldiers.

The White House account of the call said: “President Biden made clear that the United States will act firmly in defense of its national interests in response to actions by Russia that harm us or our allies.”

The White House spokeswoman, Jen Psaki, said that Biden had also expressed opposition to the Nord Stream natural gas pipeline, as being a “bad deal” for Europe, one example of continuity with the Trump and Obama administrations.

The Biden team is seeking to take a tougher line on Russia’s violations of human rights and international law while seeking to make progress on arms control with Moscow, which crumbled under the Trump administration.

The two leaders formally exchanged notes extending the 2010 New Start agreement by five years, assuring the survival of the last remaining arms control treaty between the US and Russia in the wake of the Trump era.

The extension was agreed just 10 days before New Start was due to expire. It keeps in place a limit of 1,550 deployed strategic warheads on either side, imposes limits on delivery systems, and enforces verification and transparency measures, helping ensure the two biggest nuclear weapons powers do not take each other by surprise.

According to the White House the two leaders also talked about re-establishing a regular “strategic stability dialogue” between senior officials, at which frictions in the relationship, and possible new arms control agreements, could be discussed.

The Kremlin’s readout of the conversation said that “the presidents expressed their satisfaction with the exchange of notes of extension of the New Start, which happened today”.

“In the coming days the parties will complete all the necessary procedures to ensure that this important international legal mechanism for the mutual limitation of nuclear missile arsenals functions in the future,” the Kremlin account said.

The Kremlin’s account described the conversation as “frank and businesslike” – a turn of phrase often used to describe tense discussions.

It added that the two leaders had also discussed the Open Skies treaty, another arms control agreement allowing transparency through mutual aerial surveillance, which Trump also withdrew from, and from which Moscow has said it was also preparing to leave.

Biden and Putin discussed the 2015 nuclear deal with Iran, which Trump left but Biden has said he is willing to rejoin, and the conflict in Ukraine between the government there and Russian-backed separatists. Putin, now dealing with his fifth US president, restated his proposal for a summit of the five permanent members of the UN security council.

Dmitri Trenin, the director of the Carnegie Endowment’s Moscow Centre, tweeted that: “[The] Putin-Biden phone conversation today promises no reset, but suggests a degree of predictability to the badly strained relationship. Confrontation needs to be managed safely.”

Related: How Joe Biden’s cold war experience will shape his approach to Russia

The change in course in US foreign policy is likely to accelerate after the Senate confirmed the appointment of Antony Blinken as secretary of state on Tuesday, one of his first actions was to co-sign a statement with other G7 foreign ministers condemning the poisoning and arrest of Navalny and the mass detention of protesters and journalists.

The statement said the G7 ministers “call upon Russia to adhere to its national and international obligations and release those detained arbitrarily for exercising their right of peaceful assembly”.

At the UN, the acting US ambassador announced another sharp break with Trump-era policy, the restoration of diplomatic ties with the Palestinian Authority and renewing aid to Palestinian refugees as part of its support for a two-state solution to the Israel-Palestinian conflict. Trump, a close ally of the Israeli prime minister, Benjamin Netanyahu, had broken US ties with the Palestinians.

The Biden team has said its first foreign policy goal would be to repair relations with allies and global institutions ruptured by Trump. The state department said on Tuesday it would “thoroughly review” sanctions the Trump administration imposed on the prosecutors office of the international criminal court (ICC), over investigations it launched into war crimes committed by all parties in Afghanistan, and by Israeli and Palestinian forces in the West Bank, Gaza and East Jerusalem.

“The United States shares the goals of the ICC in promoting accountability for the worst crimes known to humanity. At the same time, the United States has always taken the position that the court’s jurisdiction should be reserved for countries that consent to it, or that are referred by the UN security council,” a state department spokesperson said.

“Much as we disagree with the ICC’s actions relating to the Afghanistan and Israeli/Palestinian situations, the sanctions will be thoroughly reviewed as we determine our next steps.”