European Union spokeswoman Mina Andreeva said that Juncker watched May's announcement that she will step down as Conservative Party leader on June 7 "with emotion" and added it was "without personal joy."
She said Juncker will "equally respect and establish working relations" with May's successor. Britain currently faces an Oct. 31 deadline to leave the EU.
German Chancellor Angela Merkel has noted "with respect" the decision of British Prime Minister Theresa May to step down, and will continue to work closely with her successor for an orderly Brexit.
Merkel's spokeswoman, Martina Fietz, told reporters Friday that the chancellor and May always "worked together in a good and trusting" relationship and would continue to do so while May remains in office.
Looking ahead, Fietz says, "we, and the EU as a whole, are interested in a good solution being found in Britain" to the Brexit issue, and that means "an orderly exit."
The German government would not speculate on May's possible successor.
British Prime Minister Theresa May's departure speech is drawing praise from fellow Conservative Party members, including some who had criticized her Brexit stance.
Andrea Leadsom, who resigned as House of Commons Leader on Wednesday to protest May's Brexit plan, tweeted that May's speech was "an illustration of her total commitment to country and duty."
Leadsom, a possible leadership contender, said May "did her utmost" and praised the dignity of the prime minister's speech.
Environment Secretary Michael Gove tweeted his thanks to the prime minister. He called it, "A moving speech from a Prime Minister who deserves our respect and gratitude."
Scotland First Minister Nicola Sturgeon, a frequent critic of May, says she is worried May's decision will bring "an even more hardline" Brexit-backer to power.
Theresa May says she will step down as U.K. Conservative Party leader on June 7, sparking a contest to become Britain's next prime minister.
She will stay as caretaker prime minister until the new leader is chosen, a process likely to take several weeks.
May has bowed to relentless pressure from her party to quit over her failure to take Britain out of the European Union on schedule.
Her departure will trigger a party leadership contest in which any Conservative lawmaker can run. The early front-runner is Boris Johnson, a former foreign secretary and strong champion of Brexit.
Britain is currently due to leave the EU on Oct. 31, but Parliament has yet to approve divorce terms.
British Prime Minister Theresa May is meeting a leader of her Conservative lawmakers amid mounting speculation that she is about to announce her departure date.
The party's key backbench committee has set a showdown meeting Friday for May to agree to leave soon or face a leadership challenge.
Pressure on May to quit over her failure to get Parliament's approval for a European Union divorce deal reached critical point this week as a senior minister quit and several Cabinet colleagues expressed doubts about her Brexit bill.
Several British media outlets reported that May would agree to give up the prime minister's post June 10, sparking a Conservative leadership contest.
She could stay in office as a caretaker prime minister for several weeks until party lawmakers and members choose a successor.