The two "met as strategic partners," Pentagon spokesperson Charles Summers said in a brief statement to the press after the meeting.
"They focused their discussion on interests, rather than positions, and on the importance of US-Turkish cooperation bilaterally and as NATO allies in achieving mutual security and economic prosperity for both countries and the region," Summers said.
Summers made no mention of the spat over the US threat to halt a joint F-35 fighter jet program with Turkey if it buys Russia's S-400 missile defense system.
Washington has already frozen deliveries of aircraft and parts, saying the US aircraft system is too sensitive to be operated in tandem with the Russian equipment.
On April 2, Shanahan said he was confident Turkey would reverse course and buy the US Patriot missile defense system instead, but Ankara has made no such commitment yet.
Last week, Turkey's President Recep Tayyip Erdogan said the delivery of the S-400 system could be earlier than initially planned, according to the Hurriyet daily.
In parallel to tensions over the missile system, the US-Turkey relationship has been strained by Ankara's threat to launch an offensive in northeast Syria against the Kurdish-majority Syrian Democratic Forces, which battled the Islamic State group with backing from Western air strikes and other support.
Ankara links the SDF to the Kurdish separatist PKK movement at home, which it considers a terrorist organization.
Meeting in Washington with Turkish Foreign Minister Mevlut Cavusoglu in early April, Secretary of State Mike Pompeo warned of "devastating consequences" if Turkey strikes Syria.