China’s president, Xi Jinping, has called for Donald Trump to reach a compromise on trade, as discussions continue in an attempt to avert the imposition of heavy tariffs on goods.

Xinhua, a Chinese state-controlled news organisation, reported on Sunday that Xi told Trump in a telephone call that he had “hopes that both teams can meet each other halfway and reach an agreement beneficial to both countries and the world as early as possible”.

The presidents both expressed their willingness to implement agreements made on the sidelines of the G20 summit at the start of the month , Xinhua said.

On Saturday Trump declared he had made “big progress” in the discussion with Xi, after a week dominated by turmoil in Washington and volatility on global stock markets.

Trump wrote on Twitter that he had had “a long and very good call” with Xi regarding a possible deal.

The US had planned to increase tariffs on more than $200bn of Chinese goods from 10% to 25% in January, but Trump agreed to a 90-day delay at the start of December.

However, the potential for a ceasefire in the trade war between the US and China is likely to provide little relief for investors amid the ongoing shutdown of the US government and concerns that Trump may threaten the independence of the Federal Reserve.

Trump prompted the worst Christmas Eve on record for US stocks when he said the Federal Reserve was the “only problem our economy has”. The central bank has been raising interest rates in an effort to cool growth and forestall inflationary pressure.

The latest message from Trump on trade talks came amid a stream of invective aimed at the opposition Democrats, offering little prospect of a truce to reopen government operations. The Democrats have refused to agree a bill to fund the government that would also provide for a border wall with Mexico.

Throughout the Christmas trading week CBOE’s Vix index, the so-called fear index tracking the volatility of major US stocks on the S&P 500, remained at levels not seen since market turmoil in February.