"Unfortunately, now we see that they are not ready to advance at all. But President Putin is quite an experienced and quite a patient president of quite a patient country," Peskov said in an interview with RT's SophieCo programme hosted by Sophie Shevardnadze.
He emphasised that since the very beginning of US President Donald Trump's tenure, Putin had stressed his readiness to mend ties and to "repair" the damage that former US President Barack Obama had done to Russian-US relations.
"From the very beginning President Putin insisted that we were ready to go ahead as long and as advanced as our American counterparts are ready to," Peskov noted.
He explained that Russia and the US have many strategic matters on the agenda that can only be solved at the highest level and the absence of meetings between the two countries' presidents contradict both Russian and the US national interests.
"We see lots of strategic questions on the agenda that should be tackled on the level of two presidents. There is no way for these problems to be solved on a lower level," Peskov said.
Therefore, he noted that "not meeting each other is illogical. And it contradicts the national interests of our two countries. But we cannot be… more holy than the Pope… So that's why [Russian] President [Vladimir] Putin has said that he is going to wait."
On US sanctions
Speaking about US restrictive measures against Russia, Peskov said that the sanctions affect economic relations between Russia and China, but their sovereignty allows Moscow and Beijing to pursue their own policies, especially since not all investors are cautious about investing in Russia.
"Everything is interdependent in this world. None of the countries are free in their moves and their decisions. Every country has to balance and rebalance their activities in the field of economy because we are all interdependent. So that's why yes, of course, we can feel an influence of American sanctions in our bilateral relationship, but at the same time we are sovereign enough to take those steps which are being considered of extreme importance to us and, of course, the dimension of bilateral economic relations between Russia and China is a very significant dimension for the global economy," Peskov said in an interview.
He noted that entrepreneurs used to be very careful not only in China, but in any other country.
"Every businessman has to keep in mind all the factors, all the elements that can influence their future. So some Chinese businessmen prefer to be more careful, some of them are more pro-active in their activities, some of them are waiting, some of them are building factories, automotive factories, in Russia; and one of those will be inaugurated during the visit of [Chinese] President Xi [Jinping] to Moscow [from June 5-7]," Peskov added.
READ MORE: China Defence Minister on Trade, Taiwan: ‘We'll Fight to the End' if US Want It
According to the Kremlin spokesman, sanctions have a certain impact on various foreign investors who could potentially invest in Russia, on entrepreneurs who could possibly open their businesses there.
"Yes, some of them would prefer to be more cautious about that and, in their case, we can speak about negative influence of sanctions, but not necessarily all of them prefer to keep in mind the existing sanctions. Some of them, to the contrary, would try to take advantage of reluctant behavior of the others to take advantage of the opening markets here," Peskov said.
While Russia continues to face strict economic sanctions from the United States over the 2014 Ukraine crisis and Moscow's alleged meddling in the 2016 US presidential election, the growing economic rivalry between Beijing and Washington has reached new heights over the past few months due to a deadlock in trade talks.
On Global Internet Infrastructure
Peskov also addressed the issue of global Internet infrastructure, saying that attempts to cut Russia off it are obviously being taken, since the country is facing sanctions and illegal threats from US trade organisations.
"We have every reason to think [so]. We faced American sanctions, we faced some threats coming from international trade organizations, from American trade organizations, not international, because what they did was illegal from the point of view of international law," Peskov said.
READ MORE: The New Cold War between the US, China, and Russia
In addition, Peskov slammed the United States for waging a trade war against Chinese producers of communications services devices and for confronting Iran and stressed that Russia had to take precautionary measures, since "certain counties" could jeopardise international law.
"We understand that we have to be self-sufficient, we have to be sovereign in all our capacities. All this is also applicable to the Internet. The Internet is an international environment but, unfortunately, we are living in a world where international law can be jeopardized by certain countries. We have to take measures of precaution," the spokesman stressed.
Russian President Vladimir Putin signed on 1 May into law a bill on sustainability of the Russian segment of the Internet in case the country gets disconnected from the global network. The law will come into force in November.
