WASHINGTON — American intelligence spending could rise to nearly $86 billion, a 6 percent increase that reflects the Trump administration’s proposed boost in defense and national security spending and a renewed focus on threats from Russia and China.

The director of national intelligence, Dan Coats, released the overall proposed budget for American intelligence agencies on Monday, and the Pentagon also released its proposed intelligence spending for the fiscal year starting in October.

The budget covers expenses as diverse as spy satellites, cyberweapons and the C.I.A.’s network of overseas spies and informants. But neither the administration nor Congress releases details about the so-called black budget, which is classified.

The proposed spending increase comes despite President Trump’s sometimes tempestuous relationship with his intelligence agencies and his public comments in late January that his spy chiefs should “go back to school.” Mr. Trump clashed with his intelligence agencies after a Senate hearing in which intelligence chiefs offered assessments of Iran and North Korea that were at odds with the president’s views.