A bench of Chief Justice G Rohini and Justice Jayant Nath reserved the order on the application in which AAP government has sought a stay on proceedings on the ground that the issues involve a dispute of "federal nature" between the Centre and Delhi government and the Supreme Court has exclusive jurisdiction to deal with the matter.
"The Supreme Court is the forum for adjudication of disputes of federal nature," she said.
"If framers of the Constitution had wanted that disputes of federal nature would be dealt with by the various high courts, then there would have been no exclusive jurisdiction of the Supreme Court under Article 131 in such issues," she said.
During earlier arguments on the application, Additional Solicitor General Sanjay Jain had told the bench that Article 131 does not come in the way of jurisdiction of high courts under Article 226 of the Constitution.
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A total of 11 cases arising out of the confrontation between the LG and Delhi government are being heard together by the high court.
Delhi government had on May 28 last year approached the high court challenging the Centre's notification of May 21 giving the LG absolute powers to appoint bureaucrats in the city.
It had also challenged the July 23, 2014 notification limiting the jurisdiction of the Anti Corruption Branch to Delhi government officials only.