Story highlights Trump and Xi have yet to speak by phone

Putin to travel to China in May, analysts say Trump may join him

Hong Kong (CNN) US President Donald Trump has written to his Chinese counterpart Xi Jinping, according to the White House, the first contact the two leaders have had since Xi sent a congratulatory note for the inauguration.

Trump sent a letter to President Xi Wednesday wishing him a prosperous Year of the Rooster and saying he looks forward to developing "a constructive relationship that benefits both the United States and China," press secretary Sean Spicer said.

The two leaders have yet to speak by phone.

Trump had previously been criticized by some Chinese commentators for not recording a Lunar New Year message, although his daughter and granddaughter did attend a celebration at the Chinese embassy in Washington.

Since his election, Trump has challenged Beijing over a range of issues -- slamming its military build-up in the South China Sea, its currency and trade policies and, perhaps most controversially, upending decades of diplomatic protocol by questioning a longstanding US policy towards Taiwan.