Tomcat's RUNNING.txt which you can find in the root of the bundle states that Apache Tomcat requires Java Standard Edition Runtime Environment (JRE) to run. Minimum version of JRE depends on the version of Tomcat: for Tomcat 6.0 it is Java 5, for Tomcat 7.0 - Java 6.
However you can also use JDK because, as you probably know, it includes JRE (link). The only difference is in the configuration of environment variables. If you use JRE you should set JRE_HOME, if JDK - JAVA_HOME. Read RUNNING.txt for more details.
P.S. Web containers may require JDK in order to support JSP, because Java Compiler is required to compile Servlets which are generated from *.jsp files. Tomcat has Eclipse Java Compiler bundle so it can run on JRE and still support JSP.
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