During his "technical halt" in Frankfurt, Modi, who is on his way back after attending BRICS Summit in Brazil, spoke to the German leader from his hotel Steinberger and invited her to India for India-Germany Consultations next year.
The prime minister wished Merkel on her 60th birthday on Thursday.
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.
On her part, Merkel has invited India to participate as 'Partner' country in Hanover Trade Fair in 2015.