Johnson said he will take Britain out of the trade bloc on October 31 with or without a deal, raising fears of a damaging no-deal exit.
Foreign Secretary Dominic Raab was due to hold talks with his USA counterpart Mike Pompeo at the State Department while International Trade Secretary Liz Truss has lined up meetings with top American trade officials.
Speaking to journalists at the Irish embassy after his meeting with Mr Javid, Mr Donohoe warned the relationship between the United Kingdom and Ireland would "fundamentally change" in the event of a no-deal Brexit.
Speaking to Sky in Washington today about the meeting the Foreign Secretary said: 'He expressed his high regard for Boris Johnson as a Prime Minister and we talked about all the things that we want to do together in the post-Brexit vision for the UK.
Britain's budget watchdog warned in July a no-deal Brexit would plunge Britain into recession, with spiralling unemployment, import prices, government debt, and trade barriers while real incomes, foreign investment, and house prices tumble.
Will EU capitals look at the withdrawal agreement again, and perhaps change the terms of the Brexit negotiation mandate they have given to the European Commission in order to offer concessions?
The global trade secretary continued that her team was "fast-tracking this deal so that businesses are able to take advantage of the golden opportunity to increase trade with the U.S.as soon as possible".
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Since 2006, 11 mass shootings - not including Saturday's - have been committed by men who were 21 or younger. A hospital official says another victim of the weekend mass shooting in El Paso, Texas , has died.
Mr Donohoe said the appointment of Mr Johnson as Prime Minister had "added a new dynamic" to Brexit talks.
Trade Secretary Liz Truss is in Washington to meet figures including secretary of commerce Wilbur Ross.
He was effusive in his warmth for the United Kingdom.
'Having already laid the groundwork, we are fast-tracking this deal so that businesses are able to take advantage of the golden opportunity to increase trade with the U.S. as soon as possible'.
Mr. Pompeo gave the clearest signal to date that the Trump administration is eager to make a deal. "I think there are some risks but we can manage them", he replied.
"The US is our biggest trading partner and we have more than US$1 trillion (S$1.38 trillion) invested in each other's economies".
"We are going to tell people - citizens and businesses - when we know", he said.
"The fact is the Withdrawal Agreement has been rejected by Parliament three times and will not pass in its current form so if the European Union wants a deal, it needs to change its stance. We want to get formal talks moving quickly", she said.