Speaking at Nehru University in New Delhi as part of a state visit to the country, Joachim Gauck said the UN council should no longer be based on its post-World War II structure.
During the speech, the 74-year-old also said that Germany should take on more responsibility in the world, while adding that India also needed to engage more, particularly in terms of working to combat climate change and protecting human rights.
The comments came less than a week after the president called for more German engagement in international affairs at the opening of the Munich Security Conference, adding that the country needed to leave behind its guilt over World War II.
Germany and India are both seeking a seat on the UN Security Council, which is the main global organization responsible for conflict management and peacekeeping.
First formed in 1945, the council has five permanent members, the USA, the UK, France, China and Russia - reflecting the World War II victors.
It also has 10 non-permanent members which are elected by the UN's General Assembly and serve a two-year term.
Germany last sat on the council in 2011 and 2012 and is a candidate for membership in 2019 and 2020, according to the German Foreign Office.
"If its resolutions are to be respected and implemented by all states, the council needs to have the required authority and legitimacy," the foreign office argues on its website.
"This means it has to be representative. The council's present composition is no longer representative of a world which since 1945 has seen 142 new countries join the UN."
Over the past few years, Germany's place in the world has been much-debated as it has become Europe's economic powerhouse and looks to become more involved in military operations around the world.
On Wednesday, Germany's government approved increasing the number of soldiers sent to crisis-torn Mali to 250 Bundeswehr soldiers, up from the current limit of 180, and extended the withdrawal dates of troops in Afghanistan by 10 months.
Germany "cannot look the other way when murder and rape are a daily occurrence, if only for humanitarian reasons," Defence Minister Ursula von der Leyen told news magazine Der Spiegel last Monday.
But rankings published by the European Council on Foreign Relations (ECFR) last week placed Germany third in Europe behind the UK and France, when it comes to foreign policy.