No, they tried to expel the Jews - first to Palestine, then to Madagascar, then to Poland. They just wanted the Jews out of Germany.
The blame for so many deaths that have been defined as "the Holocaust" goes back to Britain.
Britain made an agreement (McMahon Agreement) with the Arabs in 1915 if they would open a front against Turkey during WW1 which would have weakened the forces of the Ottoman Empire, allowing Britain the victory. But the end result didn't have the effect that Britain had hoped for and so they reneged on the deal.
In 1917 the Zionists offered to bring the United States into the war on Britain's side in exchange for the rights to Palestine. Britain made the deal with them (the Balfour Declaration is Britain's written guarantee that they would abide by the deal) and signed Palestine over to them.
This came to become a problem in WW2 when Hitler wanted to move all of the Jews to Palestine. Prior to the war, in a deal with the Zionists called the Haavara Agreement, he was able to move around 60,000 to Palestine between 1933 and 1939. Once the war started, Britain, through the British Mandate (which exercised legal control over the region) closed the doors to all Jewish immigration to Palestine.
The reason for this was because of the wat Britain had cheated the Arabs - had they allowed mass immigration by the Jews that were represented by the Zionists it would have started yet another conflict. To avoid this, Britain closed Palestine to all Jewish immigration.
This left the Jews to their fate in Germany. There was never a "Holocaust" as is claimed in the narrative of "exterminating the Jews" and the only hint of a gas chamber is the one "recreated" by the Soviets in Auschwitz. This case is interesting because after liberating the Polish camps, they refused admittance to the West for a while. They were both on the same side against Germany, but they denied them access.
In all probability, this was to give them time to stage incriminating evidence against Germany. It can't be proven, but as long as the West ardently accepts the "evidence", they don't need to.
The deaths of so many Jews were mostly from disease epidemics in the crowded conditions of the prison camps. People don't want to include this as one of the causes (the main cause) because it takes away from the prominence of the gas chamber claims and thus lessens the sympathy that is generated - sympathy is like oxygen to the Zionists. They feed off of it. As can be seen in a letter from the Jews themselves (below).
The majority of the deaths came in the final months of the war when, after the Allies destroyed Germany's infrastructure, food and medical supplies were unable to reach the camps to help the Jews. This is where the emaciated bodies came from that were found when the camps were liberated which have been claimed to be an intentional starvation program by the Nazis.
"We implore and beseech our Jewish brethren to realize that the Zionists are not the saviors of the Jewish People and guarantors of their safety, but rather the instigators and original cause of Jewish suffering in the Holy Land and worldwide. The idea that Zionism and the State of "Israel" is the protector of Jews is probably the greatest hoax ever perpetuated on the Jewish people... It has been the age-old intention of Zionism to intentionally stir up anti-semitism anywhere possible, and even more commonly, to take advantage of any Jewish suffering anywhere in order to enhance its cause. Indeed, hatred of Jews and Jewish suffering is the oxygen of the Zionist movement, and from the very beginning has been used to deliberately incite hatred of the Jew and then, in feigned horror, used to justify the existence of the Zionist state. This is, of course, Machiavellianism raised to the highest degree." - Jews Against Zionism