The comments by Mr Dorji came after his meeting with Ms Swaraj on the sidelines of the BIMSTEC foreign ministers' meeting in Kathmandu.
"We hope the situation in Dokalam will be resolved peacefully and amicably," Mr Dorji told reporters.
This was the first official reaction from Bhutan after Beijing's claim that the Himalayan nation had acknowledged that Dokalam belonged to China. However, China had not offered any evidence to support its claim.
Both Ms Swaraj and Mr Dorji were in Kathmandu to attend a meeting of foreign ministers from the countries of the Bay of Bengal Initiative for Multi-Sectoral Technical and Economic Cooperation (BIMSTEC), a grouping of countries in South Asia and South East Asia.
However, there was no official word from the Indian side on what was discussed during the meeting.
"Time with a close friend and neighbour. The external affairs minister meets with foreign minister of Bhutan Damcho Dorji on sidelines of BIMSTEC Foreign Ministers' meet,"
Ministry of External Affairs spokesperson Raveesh Kumar tweeted and also posted a picture of the meeting.
The two leaders mainly discussed BIMSTEC cooperation and a range of issues in bilateral relations, Sudhakar Dalale, Joint Secretary North, said of the Swaraj-Dorji meeting.
India and China have been locked in a face-off in the Dokalam area of the Sikkim sector since June 16 after Indian troops stopped the Chinese People's Liberation Army from building a road in the area.
Ms Swaraj also met Sri Lanka's minister of state for foreign affairs Vasantha Senanayake.
During the meeting they discussed bilateral issues, mutual cooperation and matters relating to strengthening cultural linkages, Mr Dalale said.
BIMSTEC has very important role for India and greater energy needs to be injected into the BIMSTEC movement, he said.
"The BIMSTEC has made an important journey in the past two decades and we need to explore untapped resources through the regional grouping for our benefit," he said.
Bangladesh, India, Myanmar, Sri Lanka, Thailand, Bhutan and Nepal are members of the BIMSTEC.