* Trump says stands with Japan against N. Korean "menace"
* Abe agrees all options on table on N.Korea
* Trump says working with Japan on trade problems (Recasts with Abe, Trump comments at news conference)
TOKYO, Nov 6 (Reuters) - U.S. President Donald Trump on Monday said America stood with ally Japan against the North Korean "menace" and that Washington would work with Tokyo to sort out problems on trade between the world's biggest and third-largest economies.
Speaking after a summit with Japanese Prime Minister Shinzo Abe in Tokyo, Trump repeated his mantra the "era of strategic patience" was over, and that the two countries were working to counter the "dangerous aggressions" of the North Korean regime.
Trump is on the second day of a 12-day Asian trip that is focusing on both trade and North Korea's nuclear missile programmes.
Abe told the same news conference that Japan backed Trump's stance that "all options" are on the table when it comes to North Korea, saying the two countries were "100 percent" together on the issue.
Earlier, Trump vowed to push for a free and balanced trade partnership with Japan after decades of "massive trade deficits" but said relations with close ally Tokyo were "better than we have ever had".
Abe, at the start of a working lunch with Trump, offered his "heart-felt condolences" for the victims of a gunman who massacred at least 26 worshippers at a church in Texas.
White House spokeswoman Sarah Sanders said Trump, who earlier expressed grief for the victims, had no plans at this time to change the schedule for his 12-day Asian trip, which will also take him to Seoul, Beijing and Danang, Vietnam.
(reporting by Steve Holland, additional reporting by Kaori Kaneko, writing by Linda Sieg; Editing by Michael Perry)