WASHINGTON, Nov 16 (Reuters) - U.S. National Security Adviser Jake Sullivan said on Tuesday that U.S. engagement with China will intensify at multiple levels to ensure that competition between the two powers does not veer into conflict. Speaking hours after a virtual summit between U.S. President Joe Biden and Chinese counterpart Xi Jinping, Sullivan said the two leaders had agreed that "we would look to begin to carry forward discussion on strategic stability" - a reference to U.S. concerns about China"s nuclear and missile buildup. "President Biden did raise with President Xi the need for a strategic stability set of conversations...that that needs to be guided by the leaders and led by senior empowered teams on both sides that cut across security, technology and diplomacy," Sullivan said in a Brookings Institution webinar. "You will see at multiple levels an intensification of the engagement to ensure that there are guardrails around this competition so that it doesn"t veer off into conflict." Biden and Xi talked for about three and a half hours in their virtual meeting, but appeared to do little to narrow differences between the superpowers which have raised fears of an eventual conflict between them. read more The United States had envisioned the meeting, the leaders" most in-depth exchange since Biden took office in January, as a way to put stability in a relationship increasingly troubled over a litany of issues, including what Washington sees as Beijing"s aggressive actions toward self-ruled Taiwan. In the meeting Biden pressed his Chinese counterpart on human rights and Xi warned that China would respond to provocations on Taiwan.