During his "technical halt" here, Modi, who is on his way back after attending BRICS Summit in Brazil, spoke to Merkel, who extended a standing invitation to him to visit Germany for an official bilateral engagement.
Calling the German leader from his hotel Steinberger, Modi invited her to India for India-Germany Consultations (IGC) next year.
The Prime Minister wished Merkel on her 60th birthday today.
He further tweeted that "Germany is India's valued friend & I look forward to working with Chancellor Merkel to make India's relations with Germany stronger."
More From This Section
Modi, who could not meet the German Chancellor when he made a overnight stopover in Berlin while en route to Brazil because she had to go to Rio de Janeiro for the FIFA World Cup final, also congratulated her on Germany's splendid victory.
Describing the talks as "fruitful", the officials said the Prime Minister conveyed that India regards Germany as a very important partner and that his government will work closely with the German side to strengthen and deepen the bilateral strategic partnership.
Modi invited Merkel to visit India in 2015 for the third meeting of the India Germany Consultations which she accepted.
The two leaders also briefly discussed areas of bilateral cooperation including through skill development, officials said.
The two leaders agreed to meet at the earliest opportunity.
Ministry of External Affairs spokesman Syed Akbaruddin said the Prime Minister had a fruitful and frank conversation with Chancellor Merkel.
Merkel extended a standing invitation to the Prime Minister to make an official bilateral visit to Germany, he added.