TOKYO, April 15 (Reuters) - Japan's Nikkei share average climbed on Tuesday, propelled by a sharp rally for automakers after U.S. President Donald Trump hinted at granting the sector some kind of tariff reprieve.

The Nikkei gained 1% to 34,321.92, with the top eight performers all being carmakers or auto component manufacturers. The broader Topix added 1.3%.

Toyota Motor ( TM ) surged 5.2% in the morning session, buoying the Tokyo Stock Exchange's auto and parts maker index by 4.6% - making it the standout performer among the bourse's 33 industry groupings.

Sumitomo Electric Industries ( SMTOF ) led individual gains with a 6.6% jump, followed closely by a 5.9% climb in Denso ( DNZOF ) , a key supplier within the Toyota Group.

Speaking on Monday at the White House, Trump said he was considering a modification to the 25% tariffs imposed on foreign auto and auto parts imports from Mexico, Canada and other places. Those tariffs could raise the costs of a car by thousands of dollars, and Trump said car companies "need a little bit of time because they're going to make 'em here."

Despite the surge in auto-sector shares and concerns over potential trade policy reversals from Trump, the Nikkei's second straight 1% gain is likely a welcome relief for investors. Last week, they were whipsawed by extreme market swings, with alternating days of sharp sell-offs and rebounds of up to 9%.

"For the first time in a while, trading is back to what you would call normal ranges," said Kazuo Kamitani, a strategist at Nomura Securities.

At the same time he cautioned that market moves may pick up again with earnings season in Japan and the United States gathering pace this week.

Japan and the U.S. are also due to begin trade talks on Thursday in Washington.

"Trump says the aim is to get factories moved to the United States," said Kamitani. "Is that market friendly? I would say no."

(Reporting by Kevin Buckland; Editing by Sherry Jacob-Phillips)