It also took a swipe at BJP, saying for 25 years, the issue has been used "for creating social strife for attaining electoral victories".
"If all stakeholders on both sides can arrive at a mutually acceptable consensus based solution, it will go a long way in ensuring lasting peace, goodwill, mutual respect and brotherhood. Otherwise, Supreme Court should adjudicate the issue on merits," Congress' chief spokesperson Randeep Surjewala said.
"For the last 25 years, this issue has been used for attaining political power and at times for creating social strife for attaining electoral victories.
"The truth, however, is that 'dialogue' and 'mutual trust' have always been the cornerstone of India's civilisational values and our 'Ganga-Jamuni' culture," the Congress leader also said.
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The Supreme Court today said fresh attempts must be made by all parties concerned to find a solution to the Ayodhya temple dispute which is a "sensitive" and "sentimental matter".
Meanwhile, Congress MP Rajiv Shukla said that all parties involved in the dispute will go by what the court has to say.
(REOPENS DEL36)
Asked about the Ayodhya issue at the AICC briefing, Congress spokesperson Deepender Singh Hooda said the party welcomes a settlement out of the court, but if it is not possible the court is competent to give a verdict.
He said if both the sides want to settle the issue mutually through dialogue then it is welcome, otherwise the court is competent to settle the issue and give a verdict after hearing both sides.