Raut, who is the party's leader in the Rajya Sabha, has insisted that Mukherjee has proved to be the "best President" and no one can doubt his capability.
"In the last five years, he has shown that he is a capable and a non-controversial President, who is well-versed in national and international affairs," Raut said.
Asked whether the Shiv Sena, which is a key constituent of the BJP-led NDA and the oldest ideological ally of the saffron party, would appeal to other parties for backing Mukherjee for a second term, Raut said, it is a decision which only party chief Uddhav Thackeray can take.
Raut, who is the executive editor of Shiv Sena's mouthpeice Saamna, said, "Just like his party appreciated the surgical strikes by the armed forces and congratulated Prime Minister Narendra Modi, similarly, we are appreciating the good work of the President."
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When asked why is he meeting the President next week, Raut said it is just a "courtesy call".
The Sena's stand, which currently shares an uneasy relationship with the BJP, comes amid reports that the government had decided on a post-retirement home for Mukherjee, whose tenure ends in July 2017.
The Sena, under Bal Thackeray's leadership, had broken ranks with BJP to support Mukherjee's presidential candidature in 2012.