International pressure is mounting on Greece and its European creditors to reach agreement and steer the eurozone away from a potentially disastrous “Grexit”.

The US treasury secretary, Jack Lew, told Greece’s prime minister, Alexis Tsipras, and its new finance minister, Euclid Tsakalotos, that Washington “looked forward” to a swift resolution to the crisis unfolding in Europe.

Tsipras told the German chancellor, Angela Merkel, that Greece would bring a new proposal to the table at an emergency eurozone summit on Tuesday, days after Greeks voted overwhelmingly to reject the conditions of a previous bailout plan proposed by the country’s creditors.

Lew said he hoped a resolution would “allow Greece to make difficult but necessary fiscal and structural reforms, return to growth, and achieve debt sustainability within the eurozone”, a US treasury statement said.

Japan’s economics minister, Akira Amari, called on Greece and the EU to do everything possible to contain the fallout from the crisis, which on Monday sent share prices tumbling around Asia and saw losses for the euro.

Amari said all parties should strive towards a “win-win” deal that would keep Greece in the single currency, despite Greek voters’ rejection of austerity.

“Greece has already done a lot to restore fiscal discipline, such as cutting pensions and wages,” he told reporters. “I understand why the Greek people are venting their frustration. Fiscal consolidation is not making progress. They are in deflation. The world expects Greece and the EU to cooperate on a final bail out plan.”

Asian markets stabilised on Tuesday after suffering significant losses across the board the previous day, but investors remain cautious as long as doubts hang over the future of Greece’s membership of the eurozone.

Their concerns centre on the volatility in financial markets and harm to economic growth that could follow a messy Greek exit from the eurozone.

“Greece is in a difficult condition. Although there is volatility in the short term and discussion will be rough, I still expect a solution to be found to avoid a very nasty situation in the end,” said Alain Bokobza, the Paris-based head of global asset allocation at Societe Generale, who is on a visit to Tokyo.

On Tuesday Japan’s Nikkei share index had risen 1.4% by mid-morning, having fallen by 1.2% the previous day. MSCI’s broadest index of Asia-Pacific shares outside Japan, which fell to six-month low on Monday, was up 0.3%.

The euro rebounded from Monday’s one-week low to fetch $1.1044.

Greece aside, Asian stocks are also being hit by rising concerns over huge losses on Chinese mainland stock markets in recent weeks.

Emergency liquidity measures introduced by Beijing over the weekend failed to halt volatile market movements, as Chinese shares fell again on Tuesday, casting doubt on the government’s ability to stabilize markets in the world’s second-biggest economy.

“We need to continue monitoring China shares carefully because to Japan, China could be a real risk if its market falls further,” said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.

Fujito warned that prolonged turmoil in Chinese stocks could lead to a slowdown in domestic consumption, which would adversely impact Japanese shares that are most exposed to movements in the Chinese economy.