She said the post was not symbolic and that capability and experience must supersede all other considerations.
In an appeal to the electorate comprising Lok Sabha and Rajya Sabha members and legislators in state assemblies, she said the post was responsible for "safeguarding and defending" constitutional principles.
"The values I hold dear - of inclusiveness, social justice and pluralism - are the values the president must uphold as the supreme representative of our nation," she said.
"India can then not hope to achieve the progressive modernity envisioned by its founding fathers and reflected in the collective will of its people," she said in a statement.
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Kumar said the post embodied the diversity of India's socio-political culture and the vision of its "composite ideology".
"It transcends the considerations of caste, religion or region," she said.
The post, the former minister stressed, was not symbolic.
"It articulates, in the fullest sense, the basis of our electoral philosophy - that capability and experience must always supersede all other considerations," she said.
Kumar, a dalit who was a Union Minister in the UPA government, said she was honoured to be the joint opposition candidate.
She also expressed her gratitude to Congress president Sonia Gandhi and leaders of 17 political parties for their decision to nominate her.
Kumar also individually spoke to leaders of various opposition parties to thank them for the nomination.
The presidential election will be held on July 17 and it will be a dalit vs dalit contest with Kumar pitted against NDA nominee Ram Nath Kovind.