Signs of a thaw were evident in U.S. trade negotiations with Japan this week even though the two sides remain far apart on some issues and it could take time for an agreement to be reached.

“The president’s trade team is, again, moving at (Donald) Trump speed as quickly as they can to ensure that these deals can be made,” White House press secretary Karoline Leavitt said at a briefing on Tuesday, noting that the trade team has received 18 written proposals from trading partners and is meeting with delegations from 34 countries this week.

According to press reports in the United States, preliminary trade deals could soon be signed with Japan and India, although these would be more like road maps to further negotiation rather than finalized agreements.

Markets reacted positively to indications that the trade war, started last month with a volley of tariffs by Trump, is starting to cool, and also to reassurances by Trump that he would not try to oust U.S. Federal Reserve Chairman Jerome Powell.

The 225-issue Nikkei average rose about 1.89% on Wednesday following a 2.51% rise by the S&P 500 index and a 2.71% increase for the Nasdaq Composite index in the United States on Tuesday. The dollar strengthened.

“There’s now a faint light visible — meaning that we’re starting to get a vague sense of the contours of the negotiations,” Ryosei Akazawa, Japan’s lead trade negotiator, told reporters on Monday.

"There’s still a considerable gap between the two sides, so it’s not necessarily the case that the outlook is bright,” he added. He has said previously that Japan is in no rush.

Akazawa met with Trump and his trade negotiators last week in Washington to start formal negotiations. They reportedly talked about Japan paying more for U.S. troops stationed in the country, importing more American cars and reducing the U.S. trade deficit.

Trump told Akazawa that his intention is to reduce the trade deficit to zero, according to press reports.

During a meeting on Wednesday in Tokyo, Akazawa told U.S. Ambassador to Japan George Glass that he hopes an agreement on tariffs is achieved as soon as possible. Glass said he will cooperate with Japan on the negotiations.

Japan has so far engaged in a charm offensive aimed at staying onside while politely poking holes in Trump's arguments and expectations and discreetly discrediting his assumptions.

“When there’s concern that the U.S. president or Cabinet members may be misunderstanding certain facts, we make multiple attempts to correct the record through official channels,” Akazawa said at a news conference on Tuesday.

“However, despite these efforts, there are times when their understanding doesn't really change. In such cases, we continue to point out the facts as needed, carefully and persistently.”

Since the meeting in Washington, Japan has been working on proposals to bring about the next talks, which are scheduled for later this month. TV Asahi reported Wednesday that Akazawa might fly to Washington again as early as April 30.

According to press reports, Tokyo’s potential offers include the importing of more soybeans, rice and liquefied natural gas from the U.S., as well as relaxing safety rules for U.S.-made vehicles to address Trump's claims that Japan’s testing standards put American automakers at a disadvantage.

Tokyo expanded its trade team on Monday to include senior officials from the agriculture and transportation ministries.

"We need the final package — what both sides walk away with — to be something that is not a loss for Japan. The U.S. side is obviously thinking the same, which is why negotiations become more intense as they progress," Akazawa said on Monday.