Cold War tensions certainly existed before the construction of the Berlin Wall in 1961. However, the wall certainly increased those tensions. Most of all, the presence of the Berlin Wall was a physical sign of the Cold War and a symbol of the divide between Eastern Europe and Western Europe. It stood for the difference in communist and capitalist ideology. Its purpose really depended on who you asked at the time. Was it a wall built to protect those within it or to imprison them? At any rate, it marked the border between the two ideologies in Europe.

To the West, the wall was a symbol of the tyranny and oppression of the communists. It distinctly defined the frontier between freedom and despotism. When President Reagan famously called on Premier Gorbachev to "tear down this wall" in 1987, he was ratcheting up Cold War rhetoric. The Soviet Union interpreted the speech to be "openly provocative, war-mongering."

The Berlin Wall was more of a symptom, or perhaps a symbol, of Cold War tensions than a cause. It was constructed in the wake of a crisis in Berlin in 1961 caused by the massive out-migration of East Germans into the West, where standards of living were higher. This situation nearly led to an armed conflict between the United States and the Soviet Union in the fall of 1961, and the wall was an attempt by the East Germans and their Soviet backers to stop the flow of people into the West and thus reduce tensions and lessen the likelihood of conflict. In fact, the Wall was a fairly effective solution to tensions in Europe, which had simmered throughout the 1950s. After 1961, Cold War conflicts shifted to places like Cuba, Africa, and Southeast Asia, while both sides in Europe essentially accepted the border it represented. Over time, the Wall became a symbol of communist oppression. It was despised by people on both sides, and its "fall" in 1989 marked the beginning of the end for the Soviet bloc in Europe. But it is difficult to argue that the Wall itself heightened tensions between the two sides.

President Kennedy, though profoundly hostile towards the construction of the Berlin Wall, did not directly challenge the Soviets. In truth, he couldn't, because the potential consequences of armed conflict would have been catastrophic. In some respects, the building of the wall worked to the benefit of the United States and its allies. For one thing, the Berlin Wall was a huge propaganda gift. For almost forty years, it stood as a symbol of the evil of communist tyranny, a monument to an inhumane ideology that separated families and friends, and brutally cut down anyone trying to seek a better life. On a geopolitical level, the construction of the Berlin Wall took the sting out of East-West tensions, representing, as it did, a tacit acceptance, on the part of the Soviets, of a recognizable Western sphere of influence in Europe.

Historians argue that the construction of the wall actually did more to reduce Cold War tensions than to raise them.  It took the pressure off of the Soviets to do something about the fact that millions of East Germans were escaping to West Berlin.  The East German government had been pushing the Russians to take West Berlin from the Western Allies.  The wall solved this.

If you have to argue that the wall raised tensions, you can say that it increased Western animosity towards the communists.  You can say that it made the West feel even more strongly that communism was an evil system.  This made them more likely to resist communist expansion and increased tensions.