"Do not speculate as long as there is no verified information. I hope the whole world will give thought to the feelings of the families of the 239 people who were on board the aircraft," said Rosmah, who is wife of Prime Minister Datuk Seri Najib Tun Razak.
She said anyone with credible information on the tragedy should come forward to assist efforts to trace the plane which has been missing since March 8.
"Don't throw stones and then hide your hands behind your back (make wild allegations). That's cowardice, don't just talk and not provide solutions," she said during an interview on BernamaTV's "Ruang Bicara" programme.
Flight MH370, carrying 227 passengers and 12 crew, left KL International Airport at 12.41am on March 8 and disappeared from radar screens about an hour later while over the South China Sea.
It was to have landed in Beijing at 6.30am on the same day.
A multinational search was mounted for the Boeing 777-200 aircraft, first in the South China Sea and then, after it was learnt that the plane had veered off course, in the southern Indian Ocean.
Rosmah said as a woman and mother, she felt for the families involved who wanted answers to what happened to their loved ones.
Recalling her meeting with some of the families, she said some begged her for answers as to what actually happened.
However, she said she was deeply saddened that she could not help in providing them the answers.
"I felt helpless...I wanted to help but could not. All I could do was to try to comfort them," she said.
Asked of her initial reaction on hearing about the plane, Rosmah said she was in a state of sadness and shock.
"I was shocked, my knees were shaking, my whole body felt weak, I started fervently praying that the plane would be quickly found," she said.
She said her first thoughts were that the aircraft might have experienced mechanical problems.
Rosmah praised the dedication of the search teams involved in efforts to locate the missing jetliner which entered its 38th day.
"Place your trust in the people who are tirelessly working to find the plane," she said.
She added that because of the close relations Malaysia had with many countries, they did not hesitate to help out in the search for MH370 and offered a multitude of assets and sophisticated equipment.
Rosmah also shared with the audience about the telephone conversations Najib had with foreign leaders regarding the matter.
"Even before he could finish what he wanted to say, many of the leaders straight away informed him of their willingness to help and asked what they could do," she said.
The search effort at one stage saw the participation of up to 26 countries and it now has become the biggest search operation in aviation history.
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